Question

How do you find the amplitude and period of `y=3sin(2t)`?

Answer 1

Amplitude: 3
Period: `pi`

Explanation:

graph{y=3sin(2x) [-5.46, 14.54, -4.28, 5.72]}

Considering the `x`-axis to be the time as the wave progresses and the `y`-axis the displacement, the period can be seen to be `pi` as that is the time taken for one complete oscillation

(Proof)

`y=0`

`0=3sin(2t)`

`0=sin(2t)`

`2t=sin^-1(0)`

`2t=0,pi,2pi,3pi,4pi ...`

`t=0,1/2pi,pi,3/2pi,2pi ...`

(every second time the wave crosses the `x`-axis is a complete oscillation)

`t=0,pi,2pi ...`

The constant difference is `pi`
`therefore` the period is `pi`

The amplitude is the maximum distance from the rest point of a wave - this is the same as the maximum value of the graph.

`y=sinx` has a range of `-1<=y<=1`
(the maximum value possible is 1)

This makes the maximum value of `3sin(2t) = 3(1) =3`
`therefore` the amplitude is 3