A simple harmonic oscillator consists of a block of mass 2.00 kg attached to a spring of spring constant 120 N/m. When t = 2.50 s, the position and velocity of the block are x = 0.133 m and v = 4.290 m/s. (a) What is the amplitude of the oscillations? What were the (b) position and (c) velocity of the block at t = 0 s?

w = sqrt(k/m) = sqrt(120/2) 

w = 7.75

I have the position function for x

x(t) = A cos (wt   phi) ; where A=amplitude, w=omega, t=time(2.5s), 

Not sure what phi is, or why we include it, but I need it.

V(t) = dx/dt = -Aw sin(wt   phi)  ; where A=amplitude, w=omega, t=time

So I think it's supposed to be: V(t)/x(t)

which gives us (The A's cancel):

V/x = [   - Aw sin(wt   phi)   ]   / [A cos(wt   phi  ]  

v/x = -w tan(wt   phi)   

Move -w over:

-v/xw = tan(wt   phi)

arctan(-v/xw) = wt   phi

[ arctan(-v/xw) ]  / [w t] = phi ; where v= 4.290m/s, x=.133m, w=sqrt(k/m), t = 2.5

So I get phi = .8

So the answer to C. Should be phi = .8?? but apparently that's wrong??

Anyways moving on with phi = .8

putting phi back into position function

x = A cos(wt   phi) ; where x=.133, A=?, w=7.75, phi=.8;

A = x  / [cos(wt   phi)]

For A, I get

.133 / [cos (7.75 * 2.5   .8)]

A= .547 

So the answer for part A should be Amplitude a = .547m? (This is also wrong)