In this assignment the boldface n is a parameter based on the last digit of your student number.
n is obtained by taking the last digit in your student number and adding 2.
Eg. If your student number is 3216385, then take the last digit 5 and add 2 to get n=5+2.
1. The temperature u(x,t) within a particular rod of length n with insulated ends is governed by the following boundary value problem
∂u ∂2u ∂u(0,t) ∂u(n,t) x, 0<x<1 ∂t =n∂x2, ∂x =0= ∂x and u(x,0)= 0, 1<x<n
Use the separation of variables method with u(x,t) = X(x)T(t) to determine the temperature along the rod for t > 0.
2. The vibrations along a particular beam u(x, t) with simply supported ends is governed by the following boundary value problem,
u(0,t) = 0 = ∂2u(0,t) ∂x2
u(n,t) = 0 = ∂2u(n,t) ∂x2
∂2u + n2 ∂4u = 0, ∂t2 ∂x4
u(x,0) = f(x)
Use the separation of variables method with u(x,t) = X(x)T(t) to find an expression
for the eigenvlaues λn. (8 marks)
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