An object oscillates with an angular frequency of 8.0 rad/s. at t = 0, the object is at x0 = 4 cm with an initial velocity v0 = -25 cm/s. find the amplitude and the phase constant for the motion.

Explanation:

We have here a simple harmonic motion, so the equation of the position in this motion is:  

(1)

A: Amplitude

ω: angular frequency

φ: phase constant

If we take the derivative of x with respect to t from (1), we can find the velocity equation of this motion:

(2)

Let's evaluate (1) and (2) in t=0.

(3)

(4)

Dividing 4 by 3 we have:

Now, using (3) we can find the amplitude.

I hope it helps!