NOTE: Please show your work, I\'m trying to understand the math behind this and

Question

NOTE: Please show your work, I'm trying to understand the math behind this and I won't give points for only answers. I can't find any help online and I searched extensively before deciding to post here. I DONT WANT JUST THE ANSWERS.

A block with a mass of 0.800 kg is connected to a spring, displaced in the positive direction a distance of 50.0 cm from equilibrium, and released from rest at t = 0.The block then oscillates without friction on a horizontal surface. After being released, the first time the block is a distance of 10.0 cm from equilibrium is at t = 0.200 s.

Explanation / Answer

m = 0.8 kg, A = 0.500 m, at t = 0.200 s, x = 0.1 m,
a) x = Acos(?t)
?cos(?t) = x/A = 0.100/0.500 = 0.2
?t = 1.369 rad
? = 1.369/0.2 = 6.847rad/s
period T = 2?/? = 0.917 s
b) ? = ?(k/m)
?k = m?2 = 37.5 N/m
c) x = Acos(?t)
v = dx/dt = -A?sin(?t) = -3.35 m/s
d) a = -?2x = -4.688 m/s2

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