Simple Harmonic Motion Question

[NanoTech]

A body oscillates in SHM according to the equation, x = A cos(wt + f) where A = 8.8, ω = 1.070, and φ = 0.420. Assume all quantities are in SI units. What is the period?

I dont know how to get the period from this equation? Can anyone lead me in the right direction, please? Thanks! ~Dave W.

[gnome]

First, I will re-write your equation to avoid confusion:

x = Acos(\omega{t} + \phi)

where the quantities are as you stated.

Now, I can tell you that \omega (the angular frequency) is equal to 2\pi{f}, where f is the frequency (number of oscillations per second).

From that, can you find the period?

[NanoTech]

Kinda. I see that f = \frac{1}{T}

So, from that, I can write:

x = Acos(\frac{2\pi}{T}(t) + \phi)

Then, I solve for T:

but i've now introduced an "x" and a "t" into the problem, where do i go from here?

[Doc Al]

Kinda. I see that f = \frac{1}{T}
Right!
So, from that, I can write:

x = Acos(\frac{2\pi}{T}(t) + \phi)
Don't do that! Instead write the equation for ω (which is given) in terms of T. (I know you can do it, since that's what you just did to rewrite that equation.)