Question

For the simple harmonic motion equation d=2sin(pi/3t), what is the frequency?

Answer 1

the answer is simply

1/6

Answer 2

Frequency of
`d=2\sin ((\pi t)/(3))` is
`(1)/(6)`.

Explanation:

We have the harmonic equation as,
`d=2\sin ((\pi t)/(3))`.

It is known that,

If a function f(x) has a period P, then the function cf(bx) has period
`(P)/(|b|)`.

So, we have,

As the function
`\sin t` has
`2\pi`, then
`d=2\sin ((\pi t)/(3))` will have period
`(2\pi)/((\pi)/(3))` = 6

Further, the frequency of a function is the reciprocal of its period.

Thus, the frequency of
`d=2\sin ((\pi t)/(3))` is
`(1)/(6)`.