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displacing the string into the form of the curve y = x(50 - x) and also by
imparting a constant velocity V to every point of the string in the position at time
t = 0. Determine the displacement function y(x, t).

Module VI 1
A rod of length 50 cm has its ends A and 8 kept at 20°C and 70°Crespectively (10)
until steady state temperature prevail. The temperature at each end 15
thensuddenly reduced to zero temperature and kept so. Find the resulting
temperature function u(x,t) taking x = 0 at A.

OR

A bar 10 cm long with insulated sides has its ends A and B maintainedat 50°C (10)
and 100°C respectively until steady state conditions prevail. The temperature atA
is suddenly raised to 90°C and at the same time that at B is lowered to 60°C. Find

thetemperature distribution in the bar at time t.
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