# Very easy simple harmonic motion question that I keep getting wrong

## Homework Statement

In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the following expression, where x is in centimeters and t is in seconds.

x = (7.00 cm) cos(4t + π/6)

At t = 0, what is its velocity?

## Homework Equations

v(t) = -A sin(ωt + ϕ)

## The Attempt at a Solution

It first asked me to find the position so I did that easily by plugging in for time and getting an answer. And to get velocity I just had to take the derivative of the initial function and then plug in once again. However, when I do this I do not get the correct answer and I can't figure out why.

v(t) = -7.00 cm sin (4(0) + π/6)

This basicaly breaks down to -7.00 * 1/2 right?

When I do this I get -3.5 cm/s and it says my answer is off by more than 10%. No idea what I am doing wrong.

cepheid
Staff Emeritus
Gold Member

## Homework Statement

In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the following expression, where x is in centimeters and t is in seconds.

x = (7.00 cm) cos(4t + π/6)

At t = 0, what is its velocity?

## Homework Equations

v(t) = -A sin(ωt + ϕ)

## The Attempt at a Solution

It first asked me to find the position so I did that easily by plugging in for time and getting an answer. And to get velocity I just had to take the derivative of the initial function and then plug in once again. However, when I do this I do not get the correct answer and I can't figure out why.

v(t) = -7.00 cm sin (4(0) + π/6)

This basicaly breaks down to -7.00 * 1/2 right?

When I do this I get -3.5 cm/s and it says my answer is off by more than 10%. No idea what I am doing wrong.

The expression in red above is not correct. It should be:

v(t) = -Aωsin(ωt + ϕ)

Since you know how to take a derivative, you can verify this for yourself. You can also see that the units work out in this case. The amplitude of the velocity has to have units of cm/s, not just cm.

gneill
Mentor
Check your derivative carefully. While d/dt cos(t) = -sin(t), d/dt cos(ωt) ≠ -sin(ωt)...

Ah ok I was forgetting to multiply my Amplitude by ω

Got it thanks