a spring-mass system is executing simple harmonic motion. What is the ratio of t

Question

a spring-mass system is executing simple harmonic motion. What is the ratio of the kinetic energy to the spring potential energy when the stretch is half of the amplitude of the motion a spring-mass system is executing simple harmonic motion. What is the ratio of the kinetic energy to the spring potential energy when the stretch is half of the amplitude of the motion a spring-mass system is executing simple harmonic motion. What is the ratio of the kinetic energy to the spring potential energy when the stretch is half of the amplitude of the motion

Explanation / Answer

At maximum compression,

Etot = 1/2 k xmax^2

At half compression,

Etot = PE + KE

As PE = 1/2 k (xmax/2)^2

Etot = 1/2 k (xmax/2)^2 + KE = 1/2 k xmax^2

Thus,

KE = 3/8 k xmax^2

Thus,

KE/PE = 3   [ANSWER]

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