Question

A vibration in a flying car is modeled with the equation below: 3sin(800pi(t-3)) where t = seconds How many cycles does it complete in 2 minutes? What is the frequency of the vibration in Hz?

Answer 1

To complete a cycle the argument of the sine function must be
`2\pi`,we're only dealing with the argument here so no need to worry about what's outside of the sine function.
In two minutes there are 120 seconds so plugging this in the argument will give us:

`800\pi(120-3)=800\pi(117)=93600\pi`
Now dividing by
`2\pi` we get:

`(93600\pi)/(2\pi)=46800cycles`
For the second question we have:

`(46800cycles)/(120sec)=(390cycles)/(1second)=390Hz`