# Math Help - [SOLVED] finding w for a tuning fork with 528 vibrations per second

1. ## [SOLVED] finding w for a tuning fork with 528 vibrations per second

A point on the tip of a tuning fork vibrates in harmonic motion described by the equation d = 14 sin wt. Find w for a tuning fork that has a frequency of 528 vibrations per second.

Please help... i'm struggling with this math analysis class (calculus/ trig.) and my teacher is hella smart... so when you ask him for help he makes you look dumb so please help. I dont know how to solve this equation with time?

3. Originally Posted by ryangrw
A point on the tip of a tuning fork vibrates in harmonic motion described by the equation d = 14 sin wt. Find w for a tuning fork that has a frequency of 528 vibrations per second.
Hey, please raise your concern with your teacher. He will probably explain it clearer if you have trouble keeping up. Usually teachers skip steps when explaining because they assume you understand, ask him to explain all the steps.

d = 14 sin (wt)

Did you know simple harmonic systems can be described with this equation:

$d = A \cos (2\pi f t + \phi)$

where d = displacement A = amplitude f = frequency t = time and $\phi$ = phase

If you compare carefully that equation with the question you are given, it is evident that $w = 2\pi f$

Simply substitute your given frequency to calculate w.

To understand why simple harmonic systems can be described by the equation I have given, I suggest you start drawing some graphs and see what happens when you change each variable, preferably by hand but computer programs helps too.

4. thank you so much