Pendulum Frequency Relationships · CAP 2007 #12

Physics · mechanics

Problem

Three simple pendulums with strings of different lengths and bobs of different masses are pulled out from their position of equilibrium to angles of θ1\theta_1, θ2=2θ1\theta_2 = 2\theta_1, and θ3=3θ1\theta_3 = 3\theta_1, respectively. All angles θ1\theta_1, θ2\theta_2 and θ3\theta_3 are very small. The bobs are then released and start oscillating freely. Which answer better matches the results of measurements of the frequencies of the three pendulums? (a) f2=2f1f_2 = 2f_1 and f3=3f1f_3 = 3f_1; (b) f3=3f1f_3 = 3f_1 and f2=2f1f_2 = 2f_1; (c) f1=f2=f3f_1 = f_2 = f_3; (d) We need to know the mass of each bob to find the relationship between the frequencies; (e) We need to know the length of each pendulum to find the relationship between the frequencies.

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