A particle of mass 1 kg is hanging from a spring of force constant 100 N m - 1 . The mass is pulled slightly downward and released so that it executes free simple harmonic motion with time period T .

Question

A particle of mass 1 kg is hanging from a spring of force constant 100 N m - 1 . The mass is pulled slightly downward and released so that it executes free simple harmonic motion with time period T . The time when the kinetic energy and potential energy of the system will become equal, is T n . The value of n is ________.

TestHub · Accepted Answer

K E = P E 1 2 k A 2 - x 2 = 1 2 k x 2 x 2 = A 2 2 x = ± A 2 y = A sin ω t A 2 = A sin ω t sin π 4 = sin ω t ω t = π 4 ; t = T 8 . Thus n = 8

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