Finding the period from SHM equation x = A cos(ωt + φ)

[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 don't 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.)