Maximum speed and magnitude of the acceleration of a spring?

  • Thread starter Howard Fox
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Homework Statement


If a midpoint of a guitar string executes simple harmonic motion following the form x(t)=Asin(wt+φ), and its angular frequency is ω = 2.76 × 103 s−1 and A=1.60mm. What is then its maximum speed of the string during this motion? And what is the maximum magnitude of the acceleration of the spring?

Homework Equations


x(t)=Asin(wt+φ)
dx/dt = Aω cos(ωt + φ)
dv/dt = −Aω2 sin(ωt + φ)

The Attempt at a Solution


I know that the maximum velocity should happen when x=0 and the maximum acceleration is when displacement is greatest, but I am not sure on how to proceed. Should I set the second equation I listed above equal to zero to find the velocity and the third equation equal to 1.60mm to find the acceleration?
Thank you for your help.
 

Answers and Replies

  • #2
kuruman
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Should I set the second equation I listed above equal to zero ...
No, just look at it. The right side is maximum when the cosine is maximum. What is the maximum value of a cosine, any cosine?
 
  • #3
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No, just look at it. The right side is maximum when the cosine is maximum. What is the maximum value of a cosine, any cosine?
One?
 
  • #4
Chandra Prayaga
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What is dx/dt ?
 
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kuruman
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