A 4൧1101

०) Solve (D? + 3DD'+2D")z =x7y

Module V ee
21 A string is stretched between two fixed points at a distance of 60 cm and the

points of the string are given initial velocities where

„+ 0 < ~प > 0 ١ )10(
v= , X being the distance from an end, find the

= (60 x),30
displacement at any time t.

OR
22 A uniform elastic string of length 60 cm is subjected to a constant tension of 2
_ Kg. If 1000 ends are fixed, the initial displacement
u(x, 0) = 60x — x*,0 > ಆ 60 and the initial velocity is zero, find the ` (10)
2 displacement function w(x, ೭)
Module VI
23 Find the temperature distribution in a rod of length 2m whose end points are
maintained at temperature 0 Cand the initial temperature is (10)
F(x) = 100(2x - x7),0 > <2
OR
24 A bar 10 cm long with insulated sides has its ends A and B maintained at 50°C

கைட்‌ and 100°C respectively ರ್ಗ 51111075 prevail. The temperature of യം.
(10)
A is suddenly raised to 90°C and at the same time that at B is lowered to 60°C.

Find the temperature distribution in the bar at time t.

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