What Are the Steps to Solve Harmonic Motion Problems?

[POKETNRJSH]

Homework Statement

A particle moves along the x axis. It is initially at the position 0.27 m, moving with velocity 0.14 m/s and acceleration -0.320 m/s2. First, assume that it moves with constant acceleration for 4.50 s.
(a) Find its position.
(b) Find its velocity at the end of this time interval.
(c) Assume that it moves with simple harmonic motion for 4.50 s and that x = 0 is its equilibrium position. Find its position.
(d) Find its velocity at the end of this time interval.

Homework Equations

x=A Cos(omega*t + phi)
phi=arcTan(-v_0_/omega*x_0_)
A=sqrt(x_0_^2+(v_0_^2/omega_2_))

The Attempt at a Solution

(a) -2.34m and (b) -1.3m/s were easily solved with constant acceleration. My professor suggested the equations under number 2, stating that we need the amplitude and phi to plug into the harmonic motion equation. My problem is filling in the equations for amplitude and phi with the correct information. I'm not sure what all the naughts signify. I think they signify the various information at zero time, but I could be wrong, and he nor the book would say.

 

[Dick]

As your professor suggested, take x(t)=A*cos(omega*t+phi). You know x(0), x'(0) and x''(0). That's three equations for three unknowns, A, omega and phi. Can you find them? Differentiate x(t) twice and try it out.