The angular velocity and the amplitude of a simple pendulum are ω and a, respectively. At a displacement x from the mean position, if its kinetic energy is T and potential energy is U, then the ratio T to U is:
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Question

The angular velocity and the amplitude of a simple pendulum are ω and a, respectively. At a displacement x from the mean position, if its kinetic energy is T and potential energy is U, then the ratio T to U is:

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G1 Physics · Accepted Answer

Step 1: For SHM, the potential energy is U = ½mω²x². Step 2: Total energy is E = ½mω²a². Step 3: Kinetic energy at displacement x is T = E − U = ½mω²(a² − x²). Step 4: Therefore T/U = [½mω²(a² − x²)]/[½mω²x²] = (a² − x²)/x². Final answer: (C) (a² − x²)/x².