Engineering Mechanics

(^542) „„„„„ A Textbook of Engineering Mechanics
Fig. 26.7. Compound pendulum
–20

• 86 400 6400

h

=

∴

20 6400

1·48 km

86 400

h

×

==Ans.

EXERCISE 26.2

1. A weight of 100 N is attached to two springs of stiffness 400 N/m and 500 N/m connected
   together vertically. Determine the period of oscillation of the weight. (Ans. 1.35 s)


2. A weight of 200 N is suspended from two springs arranged in parallel. Determine the
   periodic time of the weight, if the spring constants are 800 N/m and 1000 N/m respectively.
   Also determine angular velocity of the weight. (Ans. 0·67 s ; 9·38 rad/s)


3. A pendulum having 500 mm long string is carrying a bob of mass 100 gm. Find the time
   period of the pendulum. (Ans. 1·42 s)


4. In a laboratory, a spiral spring of stiffness 1·5 N/mm is available. Find the magnitude of
   the weight, which should be hung from the spring, so that it oscillates with a periodic
   time of 1 second. (Ans. 407 N)


5. Find the number of seconds a clock would gain per day, if the acceleration due to gravity
   is increased in the ratio of 900 : 901. (Ans. 48)


6. Calculate the number of beats lost per day by a seconds’s pendulum, when its string is
   increased by 1/10 000th of its length. (Ans. – 4·32)


7. A simple pendulum gains 4 seconds per day. Determine the change in length of the
   pendulum in order to correct the time. (Ans. – 0·092 mm)


8. A second’s pendulum is taken on a mountain 1200 metres high. Find the number of beats
   it will lose or gain per day on the mountain. Take radius of the earth as 6400 km.
   (Ans. – 16·2 beats)


9. A second’s pendulum loses 10 seconds per day at the bottom of a mine. Find the depth of
   the mine. Take radius of the earth as 6400 km. (Ans. 740 m)

26.8. COMPOUND PENDULUM

A compound pendulum, in its simplest form, consists of a rigid body suspended vertically at

O and oscillating with a small amplitude under the action of the force of gravity. At some instant, let

the position of the rigid body be at its extreme position as shown

in Fig. 26.7.

Let m = mass of the pendulum

h = Distance between point of

suspension (O) and the

centre of gravity (G) of the

body.

A little consideration will show, that if the pendulum is

given a small angular displacement θ, then the moment of the

couple tending to restore the pendulum in the equilibrium position

OA

= mgh sin θ = mghθ ...(i)

...(Since θ is very small, therefore substituting sin θ = θ)