How to understand equations of simple harmonic motion

[rad0786]

hello...

I was wondering if someone can help me fully understand the equations of SHM:

x(t) = A cos (wt + theata)
v(t) = -A sin (wt + theata)
a(t) = -A cos (wt + theata)

you see... i know that A is the amplitude and that theata is the phase shift. I know that w is agular frequency, but i don't know what it does and how to find period with it.

My real problem is the t infron of w. I have no idea what that is and I have know idea how to use it in a calcuation.

Can someone please explain to me a good general vieow of how to interpret these euqations.

Thanks

 

[James R]

The frequency of the oscillations is

$$f = \omega / 2\pi$$

The period is:

$$T = 1 / f = 2\pi / \omega$$

t is the time. For example, if you want to know where the object is at t=0, just plug in the t value:

$$x(0) = A \cos(\omega \times 0 + \theta)$$
$$= A \cos(\theta)$$

 

[Calculex]

My real problem is the t infront of w. I have no idea what that is and I have know idea how to use it in a calcuation.

t is just time, of course - plotted along the horizontal axis. $\omega$ is the angular speed in radians/sec. So $\omega t$ is just the angular displacement in radians. Since one complete cycle or circle is $2\pi$ radians, $\omega t = 2\pi\nu t = 2\pi t/T$