Question

Find a model for simple harmonic motion if the position at t = 0 is 0, the amplitude is 5 centimeters, and the period is 2 seconds.

Answer 1

Answer: d = 5 sin(πt)

Step-by-step explanation: A P E X

Answer 2

`f(x)=5\sin(\pi x)`

This is one possibility fitting the criteria.

Explanation:

I was thinking about using the sine curve because we have that it starts at
`(0,0 \cdot 5)=(0,0)` and not
`(0,1 \cdot 5)=(0,5)`. The factor of 5 came from the amplitude.

So we know so far our function looks like this
`f(x)=5\sin(x)`.

However the inside will be effected since the period is 2.

`g(x)=\sin(x)` has a period of
`2\pi`.

`h(x)=\sin(bx)` has a period of
`(2\pi)/(b)`.

We want
`f(x)=5\sin(bx)` to have a period of 2 so we want to solve
`(2\pi)/(b)=2`.

So multiply both sides by b:

`2\pi=2b`

Divide both sides by 2:

`(2\pi)/(2)=b`

`\pi=b`.

So the function we have from the given information is:

`f(x)=5\sin(\pi x)`