kept so while the end A is raised to 40°C. Find the temperature
distribution of the rod at time t.
Ans:
222
1
2401
(,)40sinexp(/225)
315
n
xnx
uxtnct
n
∞
=
=+−−
∑
p
p
p
8. Find the solution of
222
/(/)utcux∂∂=∂∂ under the conditions
(a)(0,)0(,) forall .
(b)(,0)2sin forall.
utultt
nx
uxx
l
==
=
p
Ans:
222
1
(,)2sinexp(/).
n
nx
uxtn ctl
l
∞
=
=−
∑
p
p
8.13.5 One-dimensional Wave Equation
Consider the vibrations of an elastic string placed along the x-axis,
stretched to length l between two fi xed points x= 0 and x=l. First we
consider the problem when there is an initial displacement but no ini-
tial velocity (string ...
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