# Thread: Finite string Partial differential equation prob

1. ## Finite string Partial differential equation prob

Consider the following finite string problem

$\displaystyle \mu_{tt} = \mu_{xx}$ where $\displaystyle 0\le x\le 6$

$\displaystyle \mu(x,0) = f(x)$ and $\displaystyle \mu_t(6,t) = 0$ for $\displaystyle t\ge 6$ with $\displaystyle \mu(x,0) = f(x)$, and $\displaystyle \mu_t(x,0) = 0$

where
$\displaystyle f(x) = 1 - |x - 3|$, if $\displaystyle |x - 3|\le 1$ and is 0 otherwise.(sorry i dont know how to enter this as a array)

give the equation of the solution for t = 2

2. Originally Posted by r2dee6
Consider the following finite string problem

$\displaystyle \mu_{tt} = \mu_{xx}$ where $\displaystyle 0\le x\le 6$

$\displaystyle \mu(x,0) = f(x)$ and $\displaystyle \mu_t(6,t) = 0$ for $\displaystyle t\ge 6$ with $\displaystyle \mu(x,0) = f(x)$, and $\displaystyle \mu_t(x,0) = 0$

where
$\displaystyle f(x) = 1 - |x - 3|$, if $\displaystyle |x - 3|\le 1$ and is 0 otherwise.(sorry i dont know how to enter this as a array)

give the equation of the solution for t = 2
What course is this for? It looks like a straightforward separble equation. If you let $\displaystyle \mu(x,t)= X(x)T(t)$ then the equation becomes XT"= X"T or T"/T= X"/X. Since the left hand side is a function of t only and the right hand side is a function of x only, each side must be a constant. Calling that constant $\displaystyle \lambda$, we have $\displaystyle X"/X= \lamba$ or $\displaystyle X"= \lambda X$ and $\displaystyle T"/T= \lamba$ or $\displaystyle T"= \lambda T$.

However, there is a problem with the additional conditionsl. Since this equation is second order in both x and t, you need two boundary and two initial conditions. You have only one of each.

3. Its for the partial differential equations course. Im not sure how to go about doing it as I am self teaching myself the course