Three part question: An object with mass 0.240 kg is acted on by an elastic rest

Question

Three part question:
An object with mass 0.240 kg is acted on by an elastic restoring force with force constant 10.2 N/m. The object is set into oscillation with an initial potential energy of 0.150 J and an initial kinetic energy of (6.70×10^-2) J.

I've already found the amplitude to be .206m.

What is the potential energy when the displacement is one-half the amplitude?
At what displacement are the kinetic and potential energies equal?
What is the value of the phase angle if the initial velocity is positive and the initial displacement is negative?

Explanation / Answer

P.E = (1/2)kx^2 = 0.150.....get X_initial = A K.E = (1/2)mv^2 = 0.067...get V_initial = B w = (k/m)^0.5 => x = A cos(wt) + B/w *sin(wt) a) then displacement = 0.206/2 = 0.103 => P.E = (1/2)kx^2 = (1/2)*10.2*0.103^2 =0.054 J b)equate K.E = P.E to find a relation between x,v substitute in the equation of x ,v to solve for x

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