Question

A block is executing simple harmonic motion on a frictionless surface with an amplitude of .100m. At a point 0.060m away from equilibrium point the speed of the block is 0.320m/s. What is the period? What is the displacement when the speed is 0.20m/s?

Answer 1

x = .1 sin w t for example
where w = 2 pi f = 2 pi/T
then
v = .1 w cos wt

when x = .06 , v = .320, t = t1 for example
.06 = .1 sin w t1
.320 = .1 w cos w t1
so
sin w t1 = .6
w t1 = .6435 radians
.320 = .1 w cos .6435
w = 4
so
2 pi/T = 4
T = pi/2 = 1.57 seconds
I think you can take it from there.