# Maximum speed and magnitude of the acceleration of a spring?

## 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?

Related Introductory Physics Homework Help News on Phys.org
kuruman
Homework Helper
Gold Member
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?

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?

Chandra Prayaga
What is dx/dt ?

kuruman
• 