Simple Harmonic Motion
Periodic Motion:
Any motion which repeats itself after a regular interval of time is called
periodic or harmonic motion. Motions of hands of a clock, motion of earth
around the sun, motion of the needle of a sewing machine are the examples of
periodic motion.
Oscillatory Motion: If a particle repeats its motion after a
regular interval of time about a fixed point, motion is said to be oscillatory
or vibratory. i.e. oscillatory motion is a constrained periodic motion between
precisely fixed limits. Motion of piston is an automobile engine, motion of
balance wheel of a watch are the examples of oscillatory motion.
Time period: Time
taken to complete one complete oscillation is called time period.
Or, Time after which motion is repeated is called time
period.
Frequency = Frequency is the no of oscillation completed by
oscillating body in unit time
interval. Its SI unit is Hertz.
If n = frequency, T = time period, then nT=1
Simple Harmonic
Motion: If a particle repeats its motion about a fixed point after a
regular time interval in such a way that at any moment the acceleration of the
particle is directly proportional to its displacement from the fixed point at
that moment and is always directed towards the fixed point then the motion of
the particle is called simple harmonic motion.
The fixed
pint is called mean point or equilibrium point.
Characteristic of
Simple Harmonic Motion
When a particle executing SHM passes through the mean
position:
(i)
No force acts on the particle.
(ii)
Acceleration of the particle is zero.
(iii)
Velocity is maximum.
(iv)
Kinetic energy is maximum.
(v)
Potential energy is zero.
When a particle executing SHM is
at the extreme end, then:
(i)
Acceleration of the particle is maximum.
(ii)
Restoring force acting on particle maximum.
(iii)
Velocity of particle is zero.
(iv)
Kinetic energy of particle is zero.
(v)
Potential energy is maximum.
Simple Pendulum: If a point mass is suspended from a fixed support
with the help of a mass less and inextensible string, the arrangement is called
simple pendulum. The above is ideal definition. Practically a simple pendulum
is made by suspending a small ball (called bob) from a fixed support with the
help of a light string.
If the bob of a simple pendulum is slightly
displaced from its mean position and then released, it starts oscillating in
simple harmonic motion.
Time period of oscillation of a
simple pendulum is given as
T = 2π√l/g, where l is the
effective length of the pendulum and g is the acceleration due to gravity.
NOTE:- For detailed analysis of simple harmonic motion please click the link given below
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