Question

For the simple harmonic motion equation d=4sin(8pi), what is the period? If necessary, use the slash(/) to represent a fraction.

Answer 1

Step-by-step explanation:

The simple harmonic equation is given below as

`d=4sin(8\pi t)`

Concept:

The period of a sine function si calculated using the formula below

`\begin{gathered} =(2\pi)/(B) \\ where, \\ B=period \end{gathered}`

From the image below

By comparing coefficients, we will have

`\begin{gathered} (2\pi)/(B)=8\pi \\ cross\text{ multiply, we will have} \\ 8\pi B=2\pi \\ divide\text{ both sides by 8}\pi \\ (8\pi B)/(8\pi)=(2\pi)/(8\pi) \\ B=(1)/(4) \end{gathered}`

Hence,

The final answer is

`\Rightarrow(1)/(4)`