Very easy simple harmonic motion question that I keep getting wrong

  • Thread starter coldjeanz
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  • #1
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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.

The expression should read

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.

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
cepheid
Staff Emeritus
Science Advisor
Gold Member
5,192
38

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.

The expression should read

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.
 
  • #3
gneill
Mentor
20,925
2,866
Check your derivative carefully. While d/dt cos(t) = -sin(t), d/dt cos(ωt) ≠ -sin(ωt)...
 
  • #4
22
0
Ah ok I was forgetting to multiply my Amplitude by ω

Got it thanks
 

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