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01000MA102032103

Module V

⋅ ⋅ ⋅ a a
Using the method of separation of variables, solve കം = 252+ ‏له‎ where

u(x, 0) = 605%,
Find the displacement of a finite string of length L that is fixed at both ends and

is released from rest with an initial displacement f (x).

OR
Derive one dimensional wave equation.
Module VI
A rod of length 1 is heated so that its ends A and B are at zero temperature. If
⋅⋅⋅ ⋅ ⋅ ⋅ cx(l-x) ⋅
initially its temperature is given by u= ರೌ find the temperature

distribution at time t.

OR
A long iron rod, with insulated lateral surface has its left end maintained at a
temperature of 0' 0 and its right end at x = 2 maintained at 100°C. Determine
the temperature as a function of x and t if the initial temperature is

100x, 0 < « > 1
u(x, ६) = [100 1 ‏رسے ہے‎

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