Ans. Consider a mass attached with a spring. If the spring is stretched or compressed through a small displacement 'x' from its mean position, it exerts a force F on the mass.
According to the Hooke's law, this force is directly proportion to the change in Length 'x' of the spring.
F = kx ...... (1)
where k is a constant called the spring constant.
The value of k can be obtained from Equation (1) as:'' ' '
The spring constant k is defined as:
The ratio of the force acting on the spring to the increase in its length is called the spring constant .
Unit: The SI unit of spring constant is newton per metre (Nm~1).
When the spring is pulled by applying a force F, the length of the spring increases. After releasing this force, spring moves towards the mean position. During the motion, if the displacement of the mass is 'x' then
F = -k x ...... (2)
The negative sing means that the force exerted by the spring is always directed opposite to the displacement of the mass. Because the spring force always acts towards the mean position, it is called a restoring force, defined as:
A restoring force always pushes or pulls the object performing oscillatory motion towards the mean position.
Using Newton's 2nd law
F = ma
or a=£
Putting the value of F from Eq. (2), we get
-k x a=~m
Since k/m is constant, therefore a«: -x
This means that the acceleration of the body is directly proportional to its displacement from the mean position and is always directed towards the mean position. This shows that motion of a mass attached to a spring is simple harmonic motion.