Maximum speed and magnitude of the acceleration of a spring?

[Howard Fox]

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.

 

[kuruman]

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?

 

[Howard Fox]

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]

One?

One.