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Question
A string on a musical instrument is held under tension $T$ and extends from the point $x=0$ to the point $x=L$. The string is overwound with wire in such a way that its mass per unit length $\mu(x)$ increases uniformly from $\mu_0$ at $x=0$ to $\mu_L$ at $x=L$. (a) Find an expression for $\mu(x)$ as a function of $x$ over the range $0 \leq x \leq L$.
Solution
VerifiedAnswered 9 months ago
Answered 9 months ago
Step 1
1 of 4a)
Required
Determine the expression for $\mu(x)$ which is a mass per length function.
Given

$x=0$, starting point.

$x=L$, final point.

$0\leq x\leq0$, x is in the range from 0 to L.
Approach
We are given that $\mu(x)$ is a mass per length and it increases uniformly (linearly) from $(x=0)$ to $(x=L)$.
We can write the expression for linearly function $\mu(x)$.
$\mu(x)=mx+b\tag 1$
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