Engineering Mechanics

(^532) „„„„„ A Textbook of Engineering Mechanics
EXERCISE 26.1

1. A helical spring has a stiffness of 1 N/mm. What mass should be hung on it, so that it may
   oscillate with a periodic time of 1·5 second? (Ans. 56·96 kg)


2. A helical spring, of negligible mass is found to extend 0·25 mm under a mass of 1·5 kg, is
   made to support a mass of 60 kg. The spring and the mass system is displaced vertically
   through 12·5 mm and then released. Determine the frequency of natural vibration of the
   system. Take g as 9·81 m/s^2.
   Find also the velocity of the mass, when it is 5 mm below its rest position.
   (Ans. 4·98 Hz ; 358·6 mm/s)


3. A mass of 1·8 kg suspended from a spring of stiffness 45 N/mm is set in oscillation. What
   length of simple pendulum will have the same frequency of oscillation? What is the
   frequency of oscillation? (Ans. 394 mm ; 0·79 Hz)

26.3. HELICAL SPRINGS IN SERIES AND PARALLEL

Fig. 26.2.

In the previous article, we have discussed the arrangement of one helical spring only. But

sometimes two or more helical springs are used at one place in the system. It will be interesting to

know that the arrangement of helical springs may be in series or parallel as shown in Fig. 26.2 (a)

and (b).

Now consider two helical springs, in series, as shown in Fig. 26.3 (a). We know that in this

case, both the springs will be subjected to the same load.

Let s 1 = Stiffness of the spring 1, and

s 2 = Stiffness of the spring 2.

Now both the springs may be assumed to be replaced by an equivalent spring of stiffness (s)

such that

12

12 12

11 1

.

ss

ss s ss

+

=+ =

Similarly, when the two springs are arranged in parallel, then they will share the given load.

And the springs may also be assumed to be replaced by an equivalent springs of stiffness (s) such that

s = s 1 + s 2