We know that when a body is set up in vibrations from its original/mean position by external force it come backs to its mean position due to action of restring force present in the body. The motion produced here is always periodic, i.e. it repeats itself after fixed intervals of time. The motion of body is along the same path i.e. towards left of mean position and then towards right (to and fro). Such type of motion is called as oscillatory motion. One complete set of such motion is called as an ‘Oscillation’. The basic form of oscillatory motion is nothing but simple harmonic motion.
Let’s define some important terms……..!
Periodic Motion:-
A motion which repeats itself in equal intervals of time of particle is called periodic motion. The time taken by the particle to complete one oscillation is called periodic time.
Oscillatory Motion:-
A periodic motion in which particle/body repeatedly moves to and fro OR up& down along the same path about the mean position is called oscillatory or vibratory motion.
E.g-i) The motion of pendulum in a clock.
ii) Motion of balance wheel of a watch.
Period of Oscillation:-
Time taken by oscillating particle to complete one set of oscillation/vibration is known as period of oscillation. (T)
Frequency of Oscillation:-
Total number of oscillations completed by particle in given unit time (or per second) is known as frequency of oscillation. (n)
Note that, n=1/T
Let’s learn the concept in detail…..!
Consider a spring of mass ‘m’ kept on horizontal surface whose one end is fixed to wall and hanger is attached to its end through frictionless pulley as shown in a fig.
When load in the hanger increases, it is observed that the spring gets stretched up to point A and then moves back to mean position and then to another point B. This indicates that the spring is oscillating about mean position with points A and B as extreme position under action of restoring force of spring and repeats periodically. Such type of motion is known as simple harmonic motion.
Let ‘x’ be the displacement of particles of spring from the mean position which is function of time and given as,
∴ x = a sin (ωt+ α)
Where ‘a’ is amplitude of motion,
‘ω’ is angular frequency and α is phase of oscillation
Then the linear simple harmonic motion is defined as, the linear periodic motion of a body, in which the restoring force or acceleration is always directed towards the mean position and is of magnitude proportional to the displacement from the mean position, is called linear SHM.
i.e. F α –x
F= -kx
Where K is constant called force constant. In magnitude,
k= F/x
The SI unit of k is N/m.
Its dimensions are [M1 T-2 ]
In terms of angular velocity, K = mω2