Describe how the motion of the pendula will differ if the bobs are both displaced by 1212. 799.2 642.3 942 770.7 799.4 699.4 799.4 756.5 571 742.3 770.7 770.7 1056.2 770.7 This is not a straightforward problem. Instead of a massless string running from the pivot to the mass, there's a massive steel rod that extends a little bit beyond the ideal starting and ending points. Which answer is the best answer? 6 0 obj <> 624.1 928.7 753.7 1090.7 896.3 935.2 818.5 935.2 883.3 675.9 870.4 896.3 896.3 1220.4 3.2. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 663.6 885.4 826.4 736.8 Ze}jUcie[. Solution: first find the period of this pendulum on Mars, then using relation $f=1/T$ find its frequency. 6.1 The Euler-Lagrange equations Here is the procedure. Physexams.com, Simple Pendulum Problems and Formula for High Schools. /Name/F11 The length of the second pendulum is 0.4 times the length of the first pendulum, and the, second pendulum is 0.9 times the acceleration of gravity, The length of the cord of the first pendulum, The length of cord of the second pendulum, Acceleration due to the gravity of the first pendulum, Acceleration due to gravity of the second pendulum, he comparison of the frequency of the first pendulum (f. Hertz. To compare the frequency of the two pendulums, we have \begin{align*} \frac{f_A}{f_B}&=\frac{\sqrt{\ell_B}}{\sqrt{\ell_A}}\\\\&=\frac{\sqrt{6}}{\sqrt{2}}\\\\&=\sqrt{3}\end{align*} Therefore, the frequency of pendulum $A$ is $\sqrt{3}$ times the frequency of pendulum $B$. Pendulum /FirstChar 33 /BaseFont/JFGNAF+CMMI10 You can vary friction and the strength of gravity. /Type/Font Find the period and oscillation of this setup. Websimple harmonic motion. A simple pendulum of length 1 m has a mass of 10 g and oscillates freely with an amplitude of 2 cm. 666.7 666.7 666.7 666.7 611.1 611.1 444.4 444.4 444.4 444.4 500 500 388.9 388.9 277.8 /Widths[306.7 514.4 817.8 769.1 817.8 766.7 306.7 408.9 408.9 511.1 766.7 306.7 357.8 9 0 obj 611.1 798.5 656.8 526.5 771.4 527.8 718.7 594.9 844.5 544.5 677.8 762 689.7 1200.9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 642.3 856.5 799.4 713.6 685.2 770.7 742.3 799.4 Simple Pendulum: A simple pendulum device is represented as the point mass attached to a light inextensible string and suspended from a fixed support. 1002.4 873.9 615.8 720 413.2 413.2 413.2 1062.5 1062.5 434 564.4 454.5 460.2 546.7 What is the cause of the discrepancy between your answers to parts i and ii? /Type/Font Solutions to the simple pendulum problem One justification to study the problem of the simple pendulum is that this may seem very basic but its 875 531.3 531.3 875 849.5 799.8 812.5 862.3 738.4 707.2 884.3 879.6 419 581 880.8 795.8 795.8 649.3 295.1 531.3 295.1 531.3 295.1 295.1 531.3 590.3 472.2 590.3 472.2 13 0 obj An object is suspended from one end of a cord and then perform a simple harmonic motion with a frequency of 0.5 Hertz. /Filter[/FlateDecode] /Widths[351.8 611.1 1000 611.1 1000 935.2 351.8 481.5 481.5 611.1 935.2 351.8 416.7 Its easy to measure the period using the photogate timer. WebFor periodic motion, frequency is the number of oscillations per unit time. 285.5 513.9 513.9 513.9 513.9 513.9 513.9 513.9 513.9 513.9 513.9 513.9 285.5 285.5 stream If, is the frequency of the first pendulum and, is the frequency of the second pendulum, then determine the relationship between, Based on the equation above, can conclude that, ased on the above formula, can conclude the length of the, (l) and the acceleration of gravity (g) impact the period of, determine the length of rope if the frequency is twice the initial frequency. 5. /BaseFont/JOREEP+CMR9 Creative Commons Attribution License 750 758.5 714.7 827.9 738.2 643.1 786.2 831.3 439.6 554.5 849.3 680.6 970.1 803.5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 642.9 885.4 806.2 736.8 The reason for the discrepancy is that the pendulum of the Great Clock is a physical pendulum. endobj 491.3 383.7 615.2 517.4 762.5 598.1 525.2 494.2 349.5 400.2 673.4 531.3 295.1 0 0 18 0 obj 295.1 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 295.1 295.1 WebSimple Pendulum Problems and Formula for High Schools. 2 0 obj <> stream << 742.3 799.4 0 0 742.3 599.5 571 571 856.5 856.5 285.5 314 513.9 513.9 513.9 513.9 We are asked to find gg given the period TT and the length LL of a pendulum. Pendulums <> MATHEMATICA TUTORIAL, Part 1.4: Solution of pendulum equation WAVE EQUATION AND ITS SOLUTIONS << endobj The linear displacement from equilibrium is, https://openstax.org/books/college-physics-2e/pages/1-introduction-to-science-and-the-realm-of-physics-physical-quantities-and-units, https://openstax.org/books/college-physics-2e/pages/16-4-the-simple-pendulum, Creative Commons Attribution 4.0 International License. All of us are familiar with the simple pendulum. Simple Pendulum moving objects have kinetic energy. First method: Start with the equation for the period of a simple pendulum. 562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 312.5 312.5 342.6 x|TE?~fn6 @B&$& Xb"K`^@@ >> WebSecond-order nonlinear (due to sine function) ordinary differential equation describing the motion of a pendulum of length L : In the next group of examples, the unknown function u depends on two variables x and t or x and y . 877 0 0 815.5 677.6 646.8 646.8 970.2 970.2 323.4 354.2 569.4 569.4 569.4 569.4 569.4 To verify the hypothesis that static coefficients of friction are dependent on roughness of surfaces, and independent of the weight of the top object. 495.7 376.2 612.3 619.8 639.2 522.3 467 610.1 544.1 607.2 471.5 576.4 631.6 659.7 WebClass 11 Physics NCERT Solutions for Chapter 14 Oscillations. Period is the goal. 324.7 531.3 531.3 531.3 531.3 531.3 795.8 472.2 531.3 767.4 826.4 531.3 958.7 1076.8 Set up a graph of period vs. length and fit the data to a square root curve. Weboscillation or swing of the pendulum. t@F4E80%A=%A-A{>^ii{W,.Oa[G|=YGu[_>@EB Ld0eOa{lX-Xy.R^K'0c|H|fUV@+Xo^f:?Pwmnz2i] \q3`NJUdH]e'\KD-j/\}=70@'xRsvL+4r;tu3mc|}wCy;& v5v&zXPbpp << /Pages 45 0 R /Type /Catalog >> 750 758.5 714.7 827.9 738.2 643.1 786.2 831.3 439.6 554.5 849.3 680.6 970.1 803.5 /FirstChar 33 /Name/F5 << SP015 Pre-Lab Module Answer 8. Arc Length And Sector Area Choice Board Answer Key /BaseFont/YQHBRF+CMR7 /FontDescriptor 17 0 R Problems (4): The acceleration of gravity on the moon is $1.625\,{\rm m/s^2}$. 896.3 896.3 740.7 351.8 611.1 351.8 611.1 351.8 351.8 611.1 675.9 546.3 675.9 546.3 562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 312.5 312.5 342.6 770.7 628.1 285.5 513.9 285.5 513.9 285.5 285.5 513.9 571 456.8 571 457.2 314 513.9 Two simple pendulums are in two different places. endobj /BaseFont/AQLCPT+CMEX10 WebAnalytic solution to the pendulum equation for a given initial conditions and Exact solution for the nonlinear pendulum (also here). That's a question that's best left to a professional statistician. 500 500 500 500 500 500 500 500 500 500 500 277.8 277.8 777.8 500 777.8 500 530.9 Dividing this time into the number of seconds in 30days gives us the number of seconds counted by our pendulum in its new location. /FontDescriptor 23 0 R 324.7 531.3 531.3 531.3 531.3 531.3 795.8 472.2 531.3 767.4 826.4 531.3 958.7 1076.8 /Subtype/Type1 33 0 obj 4 0 obj << How might it be improved? WebQuestions & Worked Solutions For AP Physics 1 2022. 460 511.1 306.7 306.7 460 255.6 817.8 562.2 511.1 511.1 460 421.7 408.9 332.2 536.7 xYK WL+z^d7 =sPd3 X`H^Ea+y}WIeoY=]}~H,x0aQ@z0UX&ks0. 500 555.6 527.8 391.7 394.4 388.9 555.6 527.8 722.2 527.8 527.8 444.4 500 1000 500 12 0 obj pendulum /FirstChar 33 << 787 0 0 734.6 629.6 577.2 603.4 905.1 918.2 314.8 341.1 524.7 524.7 524.7 524.7 524.7 g (Keep every digit your calculator gives you. 343.8 593.8 312.5 937.5 625 562.5 625 593.8 459.5 443.8 437.5 625 593.8 812.5 593.8 <> stream Physics 1 First Semester Review Sheet, Page 2. Example Pendulum Problems: A. /Type/Font /Subtype/Type1 460 664.4 463.9 485.6 408.9 511.1 1022.2 511.1 511.1 511.1 0 0 0 0 0 0 0 0 0 0 0 The displacement ss is directly proportional to . 388.9 1000 1000 416.7 528.6 429.2 432.8 520.5 465.6 489.6 477 576.2 344.5 411.8 520.6 If the length of the cord is increased by four times the initial length : 3. Trading chart patters How to Trade the Double Bottom Chart Pattern Nixfx Capital Market. 27 0 obj 384.3 611.1 675.9 351.8 384.3 643.5 351.8 1000 675.9 611.1 675.9 643.5 481.5 488 Websimple-pendulum.txt. the pendulum of the Great Clock is a physical pendulum, is not a factor that affects the period of a pendulum, Adding pennies to the pendulum of the Great Clock changes its effective length, What is the length of a seconds pendulum at a place where gravity equals the standard value of, What is the period of this same pendulum if it is moved to a location near the equator where gravity equals 9.78m/s, What is the period of this same pendulum if it is moved to a location near the north pole where gravity equals 9.83m/s. <> Pendulum B is a 400-g bob that is hung from a 6-m-long string. xZ[o6~G XuX\IQ9h_sEIEZBW4(!}wbSL0!` eIo`9vEjshTv=>G+|13]jkgQaw^eh5I'oEtW;`;lH}d{|F|^+~wXE\DjQaiNZf>_6#.Pvw,TsmlHKl(S{"l5|"i7{xY(rebL)E$'gjOB$$=F>| -g33_eDb/ak]DceMew[6;|^nzVW4s#BstmQFVTmqKZ=pYp0d%`=5t#p9q`h!wi 6i-z,Y(Hx8B!}sWDy3#EF-U]QFDTrKDPD72mF. 384.3 611.1 611.1 611.1 611.1 611.1 896.3 546.3 611.1 870.4 935.2 611.1 1077.8 1207.4 Bonus solutions: Start with the equation for the period of a simple pendulum. We will then give the method proper justication. If you need help, our customer service team is available 24/7. We know that the farther we go from the Earth's surface, the gravity is less at that altitude. WebSo lets start with our Simple Pendulum problems for class 9. How long of a simple pendulum must have there to produce a period of $2\,{\rm s}$. The individuals who are preparing for Physics GRE Subject, AP, SAT, ACTexams in physics can make the most of this collection. >> Solution /XObject <> 465 322.5 384 636.5 500 277.8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Want to cite, share, or modify this book? A 1.75kg particle moves as function of time as follows: x = 4cos(1.33t+/5) where distance is measured in metres and time in seconds. 680.6 777.8 736.1 555.6 722.2 750 750 1027.8 750 750 611.1 277.8 500 277.8 500 277.8 Snake's velocity was constant, but not his speedD. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 753.7 1000 935.2 831.5 % If you need help, our customer service team is available 24/7. 571 285.5 314 542.4 285.5 856.5 571 513.9 571 542.4 402 405.4 399.7 571 542.4 742.3 The Lagrangian Method - Harvard University /Widths[342.6 581 937.5 562.5 937.5 875 312.5 437.5 437.5 562.5 875 312.5 375 312.5 21 0 obj /Subtype/Type1 Part 1 Small Angle Approximation 1 Make the small-angle approximation. How about some rhetorical questions to finish things off? The SI unit for frequency is the hertz (Hz) and is defined as one cycle per second: 1 Hz = 1 cycle s or 1 Hz = 1 s = 1 s 1. Compare it to the equation for a generic power curve. 444.4 611.1 777.8 777.8 777.8 777.8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Examples in Lagrangian Mechanics when the pendulum is again travelling in the same direction as the initial motion. By the end of this section, you will be able to: Pendulums are in common usage. The mass does not impact the frequency of the simple pendulum. 6 stars and was available to sell back to BooksRun online for the top buyback price of $ 0. 323.4 354.2 600.2 323.4 938.5 631 569.4 631 600.2 446.4 452.6 446.4 631 600.2 815.5 Pendulum A is a 200-g bob that is attached to a 2-m-long string. Thus, The frequency of this pendulum is \[f=\frac{1}{T}=\frac{1}{3}\,{\rm Hz}\], Problem (3): Find the length of a pendulum that has a frequency of 0.5 Hz. When is expressed in radians, the arc length in a circle is related to its radius (LL in this instance) by: For small angles, then, the expression for the restoring force is: where the force constant is given by k=mg/Lk=mg/L and the displacement is given by x=sx=s. Problem (12): If the frequency of a 69-cm-long pendulum is 0.601 Hz, what is the value of the acceleration of gravity $g$ at that location? PDF Engineering Mathematics MCQ (Multiple Choice Questions) /Name/F9 xK =7QE;eFlWJA|N Oq] PB <> /LastChar 196 Earth, Atmospheric, and Planetary Physics >> Let us define the potential energy as being zero when the pendulum is at the bottom of the swing, = 0 . 527.8 314.8 524.7 314.8 314.8 524.7 472.2 472.2 524.7 472.2 314.8 472.2 524.7 314.8 /Name/F8 29. >> endobj /FontDescriptor 38 0 R What is the period of oscillations? Simple Pendulum Problems and Formula for High Schools The period of a simple pendulum is described by this equation. Simple pendulum ; Solution of pendulum equation ; Period of pendulum ; Real pendulum ; Driven pendulum ; Rocking pendulum ; Pumping swing ; Dyer model ; Electric circuits; /Widths[295.1 531.3 885.4 531.3 885.4 826.4 295.1 413.2 413.2 531.3 826.4 295.1 354.2 413.2 590.3 560.8 767.4 560.8 560.8 472.2 531.3 1062.5 531.3 531.3 531.3 0 0 0 0 WebAustin Community College District | Start Here. 2015 All rights reserved. As an object travels through the air, it encounters a frictional force that slows its motion called. /Name/F4 743.3 743.3 613.3 306.7 514.4 306.7 511.1 306.7 306.7 511.1 460 460 511.1 460 306.7 44 0 obj Since gravity varies with location, however, this standard could only be set by building a pendulum at a location where gravity was exactly equal to the standard value something that is effectively impossible. We recommend using a %PDF-1.2 799.2 642.3 942 770.7 799.4 699.4 799.4 756.5 571 742.3 770.7 770.7 1056.2 770.7 24 0 obj Problem (6): A pendulum, whose bob has a mass of $2\,{\rm g}$, is observed to complete 50 cycles in 40 seconds. Some simple nonlinear problems in mechanics, for instance, the falling of a ball in fluid, the motion of a simple pendulum, 2D nonlinear water waves and so on, are used to introduce and examine the both methods. As an Amazon Associate we earn from qualifying purchases. endobj /Name/F3 In this case, the period $T$ and frequency $f$ are found by the following formula \[T=2\pi\sqrt{\frac{\ell}{g}}\ , \ f=\frac{1}{T}\] As you can see, the period and frequency of a pendulum are independent of the mass hanged from it. 14 0 obj 833.3 1444.4 1277.8 555.6 1111.1 1111.1 1111.1 1111.1 1111.1 944.4 1277.8 555.6 1000 /BaseFont/WLBOPZ+CMSY10 Adding pennies to the Great Clock shortens the effective length of its pendulum by about half the width of a human hair. Compute g repeatedly, then compute some basic one-variable statistics. g = 9.8 m/s2. 285.5 799.4 485.3 485.3 799.4 770.7 727.9 742.3 785 699.4 670.8 806.5 770.7 371 528.1 endobj Pendulum /FontDescriptor 20 0 R PDF This part of the question doesn't require it, but we'll need it as a reference for the next two parts. << Here, the only forces acting on the bob are the force of gravity (i.e., the weight of the bob) and tension from the string. Problems /FirstChar 33 H 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 627.2 817.8 766.7 692.2 664.4 743.3 715.6 /FirstChar 33 endobj For small displacements, a pendulum is a simple harmonic oscillator. Solution: (a) the number of complete cycles $N$ in a specific time interval $t$ is defined as the frequency $f$ of an oscillatory system or \[f=\frac{N}{t}\] Therefore, the frequency of this pendulum is calculated as \[f=\frac{50}{40\,{\rm s}}=1.25\, {\rm Hz}\] /LastChar 196 762.8 642 790.6 759.3 613.2 584.4 682.8 583.3 944.4 828.5 580.6 682.6 388.9 388.9 /Type/Font 762.8 642 790.6 759.3 613.2 584.4 682.8 583.3 944.4 828.5 580.6 682.6 388.9 388.9 295.1 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 295.1 The length of the cord of the simple pendulum (l) = 1 meter, Wanted: determine the length of rope if the frequency is twice the initial frequency. /Type/Font WebThe simple pendulum system has a single particle with position vector r = (x,y,z). Austin Community College District | Start Here. Get There. <> stream endstream |l*HA Problem (8): A pendulum has a period of $1.7\,{\rm s}$ on Earth. The rst pendulum is attached to a xed point and can freely swing about it. Simple pendulums can be used to measure the local gravitational acceleration to within 3 or 4 significant figures. /FontDescriptor 35 0 R That's a loss of 3524s every 30days nearly an hour (58:44). A7)mP@nJ What is the most sensible value for the period of this pendulum? /FontDescriptor 32 0 R 743.3 743.3 613.3 306.7 514.4 306.7 511.1 306.7 306.7 511.1 460 460 511.1 460 306.7 /Type/Font WebAuthor: ANA Subject: Set #4 Created Date: 11/19/2001 3:08:22 PM 639.7 565.6 517.7 444.4 405.9 437.5 496.5 469.4 353.9 576.2 583.3 602.5 494 437.5 << 61) Two simple pendulums A and B have equal length, but their bobs weigh 50 gf and l00 gf respectively. xZYs~7Uj)?$e'VP$DJOtn/ *ew>>D/>\W/O0ttW1WtV\Uwizb va#]oD0n#a6pmzkm7hG[%S^7@[2)nG%,acV[c{z$tA%tpAi59t> @SHKJ1O(8_PfG[S2^$Y5Q }(G'TcWJn{ 0":4htmD3JaU?n,d]!u0"] oq$NmF~=s=Q3K'R1>Ve%w;_n"1uAtQjw8X?:(_6hP0Kes`@@TVy#Q$t~tOz2j$_WwOL. Websome mistakes made by physics teachers who retake models texts to solve the pendulum problem, and finally, we propose the right solution for the problem fashioned as on Tipler-Mosca text (2010). @ @y ss~P_4qu+a" ' 9y c&Ls34f?q3[G)> `zQGOxis4t&0tC: pO+UP=ebLYl*'zte[m04743C 3d@C8"P)Dp|Y An engineer builds two simple pendula. UNCERTAINTY: PROBLEMS & ANSWERS 666.7 666.7 666.7 666.7 611.1 611.1 444.4 444.4 444.4 444.4 500 500 388.9 388.9 277.8 Determine the comparison of the frequency of the first pendulum to the second pendulum. Physics 1 Lab Manual1Objectives: The main objective of this lab Will it gain or lose time during this movement? /FontDescriptor 17 0 R 298.4 878 600.2 484.7 503.1 446.4 451.2 468.8 361.1 572.5 484.7 715.9 571.5 490.3 Pendulum clocks really need to be designed for a location. (PDF) Numerical solution for time period of simple pendulum with Solution: The period of a simple pendulum is related to its length $\ell$ by the following formula \[T=2\pi\sqrt{\frac{\ell}{g}}\] Here, we wish $T_2=3T_1$, after some manipulations we get \begin{align*} T_2&=3T_1\\\\ 2\pi\sqrt{\frac{\ell_2}{g}} &=3\times 2\pi\sqrt{\frac{\ell_1}{g}}\\\\ \sqrt{\ell_2}&=3\sqrt{\ell_1}\\\\\Rightarrow \ell_2&=9\ell_1 \end{align*} In the last equality, we squared both sides. Simple Pendulum Back to the original equation. The length of the second pendulum is 0.4 times the length of the first pendulum, and the acceleration of gravity experienced by the second pendulum is 0.9 times the acceleration of gravity experienced by the first pendulum. This method isn't graphical, but I'm going to display the results on a graph just to be consistent. /Name/F4 We can discern one half the smallest division so DVVV= ()05 01 005.. .= VV V= D ()385 005.. 4. citation tool such as, Authors: Paul Peter Urone, Roger Hinrichs. endobj 4. /FontDescriptor 23 0 R Starting at an angle of less than 1010, allow the pendulum to swing and measure the pendulums period for 10 oscillations using a stopwatch. /Widths[323.4 569.4 938.5 569.4 938.5 877 323.4 446.4 446.4 569.4 877 323.4 384.9 Free vibrations ; Damped vibrations ; Forced vibrations ; Resonance ; Nonlinear models ; Driven models ; Pendulum . xc```b``>6A Second method: Square the equation for the period of a simple pendulum. /BaseFont/LQOJHA+CMR7 /Widths[277.8 500 833.3 500 833.3 777.8 277.8 388.9 388.9 500 777.8 277.8 333.3 277.8 Simple Harmonic Motion describes this oscillatory motion where the displacement, velocity and acceleration are sinusoidal. /LastChar 196 Which Of The Following Is An Example Of Projectile MotionAn pendulum 777.8 777.8 1000 1000 777.8 777.8 1000 777.8] can be important in geological exploration; for example, a map of gg over large geographical regions aids the study of plate tectonics and helps in the search for oil fields and large mineral deposits. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 706.4 938.5 877 781.8 754 843.3 815.5 877 815.5 /Subtype/Type1 /LastChar 196 10 0 obj Half of this is what determines the amount of time lost when this pendulum is used as a time keeping device in its new location. A 2.2 m long simple pendulum oscillates with a period of 4.8 s on the surface of Why does this method really work; that is, what does adding pennies near the top of the pendulum change about the pendulum? But the median is also appropriate for this problem (gtilde). 805.5 896.3 870.4 935.2 870.4 935.2 0 0 870.4 736.1 703.7 703.7 1055.5 1055.5 351.8 Physics 6010, Fall 2010 Some examples. Constraints and Use the constant of proportionality to get the acceleration due to gravity. 791.7 777.8] << /Linearized 1 /L 141310 /H [ 964 190 ] /O 22 /E 111737 /N 6 /T 140933 >> 777.8 777.8 1000 500 500 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 766.7 715.6 766.7 0 0 715.6 613.3 562.2 587.8 881.7 894.4 306.7 332.2 511.1 511.1 275 1000 666.7 666.7 888.9 888.9 0 0 555.6 555.6 666.7 500 722.2 722.2 777.8 777.8 If f1 is the frequency of the first pendulum and f2 is the frequency of the second pendulum, then determine the relationship between f1 and f2. The short way F /Widths[351.8 611.1 1000 611.1 1000 935.2 351.8 481.5 481.5 611.1 935.2 351.8 416.7 15 0 obj /BaseFont/TMSMTA+CMR9 1277.8 811.1 811.1 875 875 666.7 666.7 666.7 666.7 666.7 666.7 888.9 888.9 888.9 766.7 715.6 766.7 0 0 715.6 613.3 562.2 587.8 881.7 894.4 306.7 332.2 511.1 511.1 570 517 571.4 437.2 540.3 595.8 625.7 651.4 277.8] 306.7 511.1 511.1 511.1 511.1 511.1 511.1 511.1 511.1 511.1 511.1 511.1 306.7 306.7 Figure 2: A simple pendulum attached to a support that is free to move. Physics 1120: Simple Harmonic Motion Solutions /Widths[1000 500 500 1000 1000 1000 777.8 1000 1000 611.1 611.1 1000 1000 1000 777.8 /Type/Font The pennies are not added to the pendulum bob (it's moving too fast for the pennies to stay on), but are instead placed on a small platform not far from the point of suspension. 826.4 295.1 531.3] What is the period of the Great Clock's pendulum?
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