# Simple Harmonic Motion

1. Nov 27, 2007

### Rubidium

1. The problem statement, all variables and given/known data
(a) Show that A$$_{0}$$cos($$\omega$$t+$$\delta$$) can be written as A$$_{s}$$sin($$\omega$$t)+A$$_{c}$$cos($$\omega$$t), and determine A$$_{s}$$ and A$$_{c}$$ in terms of A$$_{0}$$ and $$\delta$$.
(b) Relate A$$_{c}$$ and A$$_{s}$$ to the initial position and velocity of a particle undergoing simple harmonic motion.

2. Relevant equations
x=Acos($$\omega$$t+$$\delta$$)
v$$_{x}$$=-$$\omega$$Asin($$\omega$$t+$$\delta$$)

3. The attempt at a solution

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Nov 27, 2007

### Astronuc

Staff Emeritus
Start with the trigonometric identity for cosine of the sum of two angles, e.g. cos (a+b) = cos a cos b - sin a sin b, and see where that leads.

The initial position and velocity are taken at t = t0 or t = 0?

3. Dec 4, 2007

### Rubidium

I got the first part by using the trig identity and then taking the derivative, except I don't know why I had to take the derivative but it worked out anyway so I did.
Now, if t=0 then that would make the sine portion of the position 0 and the cosine portion 1 so the initial position would equal Ac, right?
For velocity, what would I do with that or is my whole idea wrong?