Question

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

Answer 1

Find the solutions for d = 0. Every 2 passes through d = 0 will be one complete vibration. From that you can determine w.

Answer 2

As d is proportional to \(\sin \omega t\), and \(\sin x\) has a period of \(2\pi\), 1 vibration/second implies \(\omega t\) goes from \(0\) to \(2\pi\) in 1 second. What does that imply about \(\omega\) when the frequency is 528 vibrations/second?

Answer 3

Well I know the period flipped is the frequency. frequency is 528 so flip is 1/528. I know period is \[\frac{ 2\pi }{ \left| b \right| }\] so \[\frac{ 1 }{ 528 } = \frac{ 2\pi }{ \left| b \right| }\] then I cross multiply to be\[\omega = (1056 \pi )rad/\sec\]is that right?

Answer 4

Looks right to me! At \(t = 1, \omega t = 1056\pi\) and that gives 528 periods in 1 second.

Answer 5

thanks so much!

Answer 6

If I graph the first 0.01 second, we get about 5 1/4 complete periods, so it must be right.