- #1

piano.lisa

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## Homework Statement

Discuss the motion of a continuous string when the initial conditions are q'(x,0) = 0 and q(x,0) = Asin(3πx/L). Resolve the solution into normal modes. Show that if the string is driven at an arbitrary point, none of the normal modes with nodes at the driving point will be excited.

## Homework Equations

**i.**q(x,0) = Asin(3πx/L)

**ii.**q'(x,0) = 0

**iii.**q(x,t) = Σ[μsin(nπx/L)cos(ωt)]

**iv.**ω = (nπ/L)[(T/μ)^(1/2)]

<the sum is from n=1 to infinity, and the ω is different for each

*n*>

<μ is a function of the amplitude>

## The Attempt at a Solution

At t=0, for

**iii**, cos(ωt)=1. Therefore, the string is oscillating with n=3. I assumed that this is the 3rd normal mode. Therefore, by

**iv**, the string is oscillating with a frequency of ω = (3π/L)[(T/μ)^(1/2)].

From this point, I do not know which method to take to find the normal modes.

I will be working on the question in the mean time. Please give any helpful suggestions. Thank you.