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:

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

This is one possibility fitting the criteria.

Step-by-step 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 $\frac{2\pi}{b}$.

We want $f(x)=5\sin(bx)$ to have a period of 2 so we want to solve $\frac{2\pi}{b}=2$.

So multiply both sides by b:

$2\pi=2b$

Divide both sides by 2:

$\frac{2\pi}{2}=b$

$\pi=b$.

So the function we have from the given information is:

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