CBSE Class 12 Physics Simple Harmonic Motion Exam Notes

CBSE Class 12 Physics Simple Harmonic Motion Exam Notes. Please refer to the examination notes which you can use for preparing and revising for exams. These notes will help you to revise the concepts quickly and get good marks.

PERIODIC AND OSCILLATORY MOTION

Periodic Motion: A motion which repeats itself after equal intervals of time is called periodic motion.Oscillatory Motion: A body is said to possess oscillatory or vibratory motion if it moves back and forth repeatedly about a mean position. For an oscillatory motion, a restoring force is required.

SIMPLE HARMONIC MOTION

Simple Harmonic Motion is a periodic motion in which a body moves to and fro about its mean or equilibrium position such that its restoring force or its acceleration is directly proportional to the displacement from its mean position and is directed towards its mean position. It can be expressed mathematically as,
F = m. d²x/dt²=-kx
Where m is the mass on which a restoring force F acts to impart an acceleration d²x/dt² along x-axis such that the restoring force F or acceleration is directly proportional to the displacement x along x-axis and k is a constant. The negative sign shows that the restoring force or acceleration is directed towards the mean position. The differential equation of a simple hormonic motion is given by,

REPRESENTATION OF SIMPLE HARMONIC MOTION :

If a point mass m is moving with uniform speed along a circular path of radius a, its projection on the diameter of the circle along y-axis represents its simple harmonic motion.
y = a sin ωt

Where ω is the uniform angular velocity of the body of mass m along a circular path of radius a such that ωt is angle covered by the radius in time t from the initial position A at t = 0 to the position B. As ∠AOB = ∠OBC = ωt, the foot of perpendicular from B to the diameter YOY ′ gives the projection at the point C such that y = OC is the projection of this body on the diameter and represents the displacement of the body executing S.H.M. along y-axis. If the body does not start its motion from the point A but at a point
A′ so that ∠AOA′ is the phase angle φ, then
y = a sin(ωt ± φ) ..... (i)
Where φ is the phase angle which may be positve or negative. The phase angle represents the fraction of the angle by which the motion of the body is out of step between the initial position of the body and the mean position of simple hormonic motion. The phase difference is the fraction of angle 2π or time period T of S.H.M. by which the body is out of step initially from the mean position of the body.
Differentiating equation (i),

EXAMPLES OF SHM

There are two types of SHM’s
1. Linear simple harmonic motion
2. Angular simple harmonic motion

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