Question

A 0.45kg object attached to a hotizontal spring oscillates in simple harmonic motion with frequency 2Hz. If the object is released from rest at x=0.05m,find velocity and acceleration at x=0.05m,0.00,and -0.005m?

Answer 1

I am not sure it is easy to understand but have a look...

Explanation:

Have a look at the general idea:

In your case: Frequency: `nu=2Hz`, Period: `T=1/nu=1/2=0.5s` and `omega=(2pi)/T=2pi*nu=2pi*2=4pi` (initial fase is zero):

`x(t)=0.05cos(4pit)`

velocity:
`v=(dx)/(dt)=-0.05*4pisin(4pit)=-0.2sin(4pit)`
`a=(dv)/(dt)=-0.2*4cos(4pit)=-0.8cos(4pit)`

These can be plotted as (with time on the horizontal axis):

I also considered your displacements and times with the corresponding values of velocity and acceleration (the last time for `x=-0.005m` is a little bit complicated...I had to improvise!).