3. a) Using convultion integral obtain the expression for the response x(t) of a SDOF system
subjected to a step input force of magnitude Fo ( 4 marks)

b) Obtain the natural frequency and mode shape of a coupled pendulum of length L and
two identical mass 'M' . The two pendulums are connected by a spring of stiffness "2K"
at a distance of 'a' from the support .
(5 Marks)
Part B

4. Show that for a vibrating system normal modes are orthogonal to each other. Using

Lagranges method obtain the stiffnes and mass matrices ofthe system shown in Fig-2 (9
marks) S. Write the matrix equation ofthe system shown below and determine the lowest
natural frequency by matrix iteration . Take stiffness between the masses 3۸۰۰

(9 Marks)

Fig-3

6. Define flexibility influence coefficients ?. Determine the flexibility matrix for a
cantilever beam of length'L' carrying four equally spaced point load of magnitude
'W' kg each.

(9 marks)

PART C
7. Find using Rayleigh's method , fundamental natural frequency of transverse vibration of
a simply supported beam of length 100 cm and of uniform cross section with moment of
inertia 40 ണ്‌. Three Loads | KN, 2 KN and 1.5 KN are acting at 25cm, 50cm and 75 cm
respectively from the left end. . Take 19.6x10° kg/cm?
( 12marks)

8. Determine the natural frequency and mode shapes ofthe spring mass system shown in
Fig 4. by the Holzer's method

12
ലല്ല
Fig-4
Take JFJ3= 0.5 kg/m 2 and JFJ4=0.125 kg/m 2,Ku=K=0.12x10°N-m/rad. ,
Kt2=0.25x | OSN-m/rad. (12 Marks)

9. a) Derive the Rayleigh's method for a uniform beam of length L and of mass of mass per
unit length p. (4 Marks)
b) Using Dunkerleys method find the fundamental frequency of transverse vibration of
a simply supported beam of length 60 cm and of uniform cross section with moment of
inertia 40 cm *. Two Loads 2 KN and 1.5 KN are acting at 20cm and 40 cm respectively
from the left end. . Take 19.6x 7۶

(8 Marks)