21.

بم

22.

23.

24.

(b)Find the particular integral of
(93 - 7DD” - 6D") 2 = sin(x + 2y) + ९५४
Module - ५
A tightly stretched homogeneous string of length 20cm with its fixed ends
executes transverse vibrations. Motion starts with zero initial velocity by
displacing the string into the form f(x) = K(x? — x?) .Find the deflection

u(x,t) at any time ர்‌.

OR
A tightly stretched string of length ‘a’ with fixed ends is initially in equilibrium
position. Find the displacement u(x, £) of the string if it is set vibrating by

giving each of its points a velocity vysin? (=)

Module - VI
Find the temperature distribution in a rod of length 2m whose end points are
maintained at temperature zero and the initial temperaturef (x) = 100(2x -
x?)
OR

The temperatures at the ends of a bar of length / cm with insulated sides are
30°C and 90°C respectively until steady state conditions prevail. If the
temperature at each end is then suddenly reduced to 0°C and maintained so,

find the temperature distribution at a distance x at time ६.