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## Homework Statement

A guitar string is vibrating in its fundamental mode, with nodes at each end. The length of the segment of the string that is free to vibrate is 0.386 m. The maximum transverse acceleration of a point at the middle of the segment is 9000 m/s^2 and the maximum transverse velocity is 3.00 m/s.

## Homework Equations

y(x,t) = A*sin(kx)*sin(wt)

dy(x,t)/dt = A*w*sin(kx)*sin(wt)

d^2y(x,t)/dt^2 = -A*w^2*sin(kx)*sin(wt)

## The Attempt at a Solution

I equated the max velocity with the secound derivative of the stading wave function.

3.00 = A*w*sin(kx)cos(wt)

Quick question: The x in the equation refers to the location on the string, not the

displacement of the string from equilibrium correct?

2nd question: is max velocity still at displacement = 0, and max acceleration at x =

1*amplitude?

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From here I tried to solve for k, first by solving for lambda.

lambda = 2L/n

lambda = 2L (because n = 1, because (sorry) f = fundemental frequency

lambda = 0.772 m

from there I solved for k

k = 2pi/lambda

k = 8.1388 /m

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using this I solved for w (omega) using w = v*k

I used max velocity for this equation

w = 24.417/s

now, does the fact this is MAX velocity effect the caluculation?

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I failed at solving for t, and I don't want to waste your time, so I won't repeat my

attempts here.

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From there I subbed the values into the equation and attempted to solve for A

(amplitude).