Physics

A mass is oscillating with amplitude A at the end of a spring.

How far (in terms of A) is this mass from the equilibrium position of the spring when the elastic potential energy equals the kinetic energy?

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  1. x=A•sinωt
    v =dx/dt = A•ω•cosωt
    PE = KE
    kx^2/2 = mv^2/2
    k = m•ω^2
    m•ω^2• (A•sinωt)^2/2 = m•( A•ω•cosωt)^2/2
    (sinωt)^2 = (cosωt)^2
    (tan ωt)^2 = 1
    ωt = π/4
    x=A•sinωt = A•sin(π/4) =0.707•A

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