Lab #6 - Google Docs - Lecture notes 6 PDF

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Stephanie Alaniz Steven Lim Shasha Tian Edgar Rojas Professor Bosco

 Lab 6: Harmonic Motions and Simple Pendulums         Due: 03/28/2017

Purpose Purpose of this lab is to use the wooden and wooden balls to prove the influence of gravity. Equipment Table Clamp, Vertical Support Rod, Meter Stick, Iron, and Wooden Balls, Vernier Caliper Procedure We first create a pendulum by hanging a spherical ball from the vertical support rod using a piece of string. By adding the radius of the ball with the length of the string, we obtain the L from the formula, T = 2 π (L/g) 0.5 . We then displace the ball from equilibrium by about 15 degrees and time how long it takes for the pendulum to make 25 complete cycles. We repeat this process using different lengths of string, and both a wooden ball and an iron ball in order to prove that while the length, or L, of the pendulum does affect the period of oscillation, the different masses of the two balls do not.

Answer of Questions: T = 2π x √（L/g) 2=2π x √（4/g) => g=4π 2 => g=39.48 m/s 2 39.48/9.8=4 So the gravity is 4 times of gravity of Earth; it’s 3 times greater than the gravity of Earth.

Conclusion Given our moderately low margin of error, it is safe to say that the data obtained proves the formula for the Period of Oscillation.

Metal Pendulum with Long String Measurements Diameter of the ball = 0.0386m Radius of the ball = 0.0193m Length of the Longer String = 0.4m Total Pendulum Length = 0.4193m Total Time for 25 Oscillations T 1 = 34.68 seconds T2 = 34.62 seconds Average Time T avg = 34.65 seconds Average Period TavgExp1 = 1.386 seconds Theoretical Period T theo1 = 2π(L/g) 0.5 = 1.30 seconds Error1 = 6.6% Metal Pendulum with Short String Measurements Length of the Shorter String = 0.2m Total Pendulum Length = 0.2193m Total Time for 25 Oscillations T 1 = 23.93 seconds T2 = 23.40 seconds Average Time T avg = 23.65 seconds Average Period TavgExp2 = 0.946 seconds Theoretical Period T theo2 = 2π(L/g) 0.5 = 0.94 seconds Error1 = 0.64%

Wooden Pendulum with Long String Diameter of the ball = 0.0381m Radius of the ball = 0.01905m Length of the Longer String = 0.4m Total Pendulum Length = 0.41905m Total Time for 25 Oscillations T 1 = 32.55 seconds T2 = 33.65 seconds Average Time T avg = 33.1 seconds Average Period TavgExp3 = 1.324 seconds Theoretical Period T theo3 = 2π(L/g) 0.5 = 1.29 seconds Error3 = 4.3% Wooden Pendulum with Short String Length of the Shorter String = 0.2m Total Pendulum Length = 0.2193m Total Time for 25 Oscillations T 1 = 23.06 seconds T2 = 23.32 seconds Average Time T avg = 23.19 seconds Average Period TavgExp4 = 0.9276 seconds Theoretical Period T theo4 = 2π(L/g) 0.5 = 0.94 seconds Error3 = 1.3%

● First Plot from left to right, represents the Metal and Wooden Balls with different masses but same Short Length of String. ● Second Plot from left to right, represents the Metal and Wooden Balls with different masses but same Long Length of String...