Simple Pendulum Lab

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Augusta University *

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1110L

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Physics

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Feb 20, 2024

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Name: Bakija Parks Online Lab 2 – Simple Pendulum Augusta Technical College PHYS 1110L 11 June 2023 Dr. Nader Copty

Objectives: The purpose of this experiment is to investigate the effects of angular displacement, mass, and length on the period of a simple pendulum. Equipment: • Pendulum bobs • String • Tape • Pencil, pen, or small rod • Scientific calculator • MS Excel • Ruler or tape measure • Smart phone • PhET Pendulum Simulation Software Theory: A pendulum that has length L, and mass m with an angle θ ; The moment of inertia I = mL^2 and the weight W = mg creates torque around the pendulum’s pivot. τ = Iα = r * F α = -L(mgsin θ ) / I (d^2* θ ) /(dt^2) = - (g/L)*sin θ With small angle: sin θ = θ ➔ (d^2* θ) / (dt^2) = - (g/L)* θ The solution to the equation yields angular frequency: w = sqrt(g/L) The period T relates to the frequency f and angular frequency w : T = 1/ f = (2*pi)/ w The period of oscillation is: T = 2*pi * sqrt(L/g) T = period of oscillation L = length of pendulum g = gravitational acceleration (9.80 m/s^2)

Part A – Simple Pendulum (Period and Angular Displacement): Trial Angle (deg.) Time for 10 oscillations (s) Exp. T (s) Acc. T (s) % Error 1 5 14.80 1.480 1.4192 4.284 2 10 14.82 1.482 1.4192 4.425 3 20 14.99 1.499 1.4192 5.623 4 30 15.59 1.559 1.4192 9.85 5 40 15.68 1.568 1.4192 10.485 • Pendulum length ( L ) = 50.0 cm Calculations Acc. T (s) = 2pi * sqrt 0.50/9.8 = 1.4192 (SAME FOR EACH TRIAL) % Error Trial 1: (1.480-1.4192)/1.4192 * 100 = 4.284% Trial 2: (1.482-1.4192)/1.4192 * 100 = 4.425% Trial 3: (1.499-1.4192)/1.4192 * 100 = 5.623%

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Trial 4: (1.559-1.4192)/1.4192 * 100 = 9.85% Trial 5: (1.568-1.4192)/1.4192 * 100 = 10.485% 1. How does the period T depend on the angular displacement? A pendulum will have the same period regardless of its initial angle. Part B – Simple Pendulum (Period and Mass): Trial Pend. Bob Time for 10 oscillations (s) Exp. T (s) Acc. T (s) % Error 1 quarter 14.1 1.41 1.4192 0.6501 2 penny 14.28 1.428 1.4192 0.6181 3 ring 14.52 1.452 1.4192 2.309 • Pendulum length (L ) = 50.0 cm • Angular displacement = 10.0 degrees Calculations Acc. T (s) = 2pi * sqrt 0.50/9.8 = 1.4192 (SAME FOR EACH TRIAL) % Error Trial 1: (1.41-1.4192)/1.4192 * 100 = 0.65% Trial 2: (1.428-1.4192)/1.4192 * 100 = 0.62% Trial 3: (1.452-1.4192)/1.4192 * 100 = 2.31% 2. How does the period T depend on the mass m ? The period does not depend on the mass of the pendulum. Part C – Simple Pendulum (Period and Length): Trial Length L (m) Time for 10 oscillations (s) Exp. T (s) Acc. T (s) % Error 1 0.200 8.89 0.889 0.898 0.958 2 0.400 12.7 1.27 1.269 0.048 3 0.600 15.45 1.545 1.555 0.623 4 0.800 18.01 1.801 1.795 0.323

5 1.000 20.1 2.01 2.007 0.145 Calculations Acc. T (s) Trial 1: 2pi * sqrt 0.2/9.8 = 0.898 s Trial 2: 2pi * sqrt 0.4/9.8 = 1.269 s Trial 3: 2pi * sqrt 0.6/9.8 = 1.555 s Trial 4: 2pi * sqrt 0.8/9.8 = 1.795 s Trial 5: 2pi * sqrt 1.0/9.8 = 2.007 s % Error Trial 1: 0.889-0.898/0.898 * 100 = 0.958% Trial 2: 1.27-1.269/1.269 * 100 = 0.048% Trial 3: 1.545-1.555/1.555 * 100 = 0.623% Trial 4: 1.801-1.795/1.795 * 100 = 0.323% Trial 5 2.01-2.007/2.007 * 100 = 0.145% 3. How does the experimental period T depend on the length L ? The period of a simple pendulum is directly proportional to the square root of length of the pendulum. 4. How do the experimental and accepted values of g compare, and what factors may cause them to be different? If the experimental value is less than the accepted value, the error is negative. If the experimental value is larger than the accepted value, the error is positive.

Conclusion: From the lab, I learned that only length of the string of a pendulum affects the oscillation period. In Part A, the pendulum was released at different angles (5, 10, 20, 30, 40) , however the result value for all trials was 1.4192 even though they were at different angles. With that being said, the angle does not play a factor in the oscillation period. In Part B, I used 3 different objects of different masses (quarter, penny, ring) . After using different objects of different masses, still the value for all trials remained the same. We can conclude that the mass of the pendulum bob does not also play a factor in the oscillation period. In Part C, the length of the pendulum was changed (.200, .400, .600, .800, 1 ), this is where we started to see a change in the result values. I got the results of 0.898, 1.269, 1.555, 1.795, and 2.007. This proves that the length of the pendulum affects the oscillation period.

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