A simple harmonic oscillator has a restoring force of 360 N/m and a mass of .59k

Question

A simple harmonic oscillator has a restoring force of 360 N/m and a mass of .59kg. It is given a KE of .2655 Joules at a point .1029 meters from equilibrium. What will be its maximum displacement from equilibrium?

Explanation / Answer

Please change the values if you cannot please comment i will do it for you.(my purpose is that you can learn.) simple harmonic oscillator m dv/dt = - k x >>>> where k = 480 N/m restorative force constant dv/dt = - (k/m) x dv = - (k/m) x.dt dv = - (k/m) x.[dx/v] >>>> v = dx/dt v dv = - (k/m) x.dx integrate v^2/2 = - (k/m) x^2/2 + c ....(1) at maximum amplitude, x = a, t=o (property of restorative force) 0 = - (k/m) x^2/2 + c >>>> c = (k/m) x^2/2 >>>(1) v^2 = (k/m) [a^2 - x^2] mv^2 = k [a^2 - x^2] Kinetic energy at any point x is KE = 0.5 mv^2 = 0.5 k [a^2 - x^2] ------(A) given at x = 0.1322, KE = 0.2496 0.2496 = 0.5 * 480*[a^2 - (0.1322)^2] 0.00104 =[a^2 - (0.1322)^2] a^2 = 0.00104 + 0.01748 a^2 = 0.01852 a = 0.1360 meter amplitude or maximum displacement of SH oscillator

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