Please help me with this physics 2 problem?

A spring (k=200N/m) lies on a frictionless table, one end connected to a wall, the other to a 4kg block. a) How much work is required to pull the block to stretch the spring .06 m? b) if block is released, find its acceleration when it has moved .02 m back toward unstretched spring position. c)Find block's velocity .02 m back toward the unstretched position. d) Find total energy in the system. e) how much time does it take the block to get to its max velocity from when it was released. f) How much would that time be changed if the spring had been stretched 2x the original stretch?



THANK SOOOO MUCH IN ADVANCE :)Please help me with this physics 2 problem?
Hello,



a). w=1/2kx2 = 1/2*(100N/m)*(0.06m)2 = 0.36j



ω = sqrt(k/m) = sqrt(200/4) = √50s^-1



A = 0.06m



in simple harmonic motion if at (t=0s) the displacement is A or -A, we use the cosine function to express the displacement (x) as a function of (t) .



X(t) = - Acos(ωt) = - 0.06cos(√50*t) , (at t=0 ,x=-A) .



V(t) = X'(t) = ωAsin(ωt) = 0.42426sin(√50*t) = ω*sqrt(A2-x2)



a(t) = V'(t) = ω2Acos(ωt) = ω2*X(t) = 50*X(t) .



b). a = 50*(0.2) = 10m/s2



c). V(t) = ω*sqrt(A2-x2) = √50*sqrt(0.062 - 0.022) = 0.4m/s



d). E = 1/2kA2 = 1/2*200*(0.06)2 = 0.36J



e). T = 2πsqrt(m/k) = 2πsqrt(4/200) = 0.88857s



the block gets to its max velocity from when it was released after T/4 seconds = 0.222s



f). it will not change. because T=2πsqrt(m/k) doesn't depend on x .