OSCILLATIONS
Frequently Asked Questions
Oscillatory motion is the motion in which a body moves repeatedly to and fro about a fixed mean position under the action of a restoring force.
Periodic motion is a type of motion that repeats itself after equal intervals of time, called the time period.
All oscillatory motions are periodic, but not all periodic motions are oscillatory because oscillatory motion must occur about a mean position.
SHM is a special type of oscillatory motion in which the restoring force is directly proportional to the displacement from the mean position and acts towards it.
A motion is SHM if the restoring force or acceleration is proportional to displacement and opposite in direction, i.e., \(a \propto -x\).
The mean position is the equilibrium position about which a body oscillates and where the net force acting on it is zero.
Amplitude is the maximum displacement of the oscillating body from its mean position.
Time period is the time taken by a body to complete one full oscillation.
Frequency is the number of oscillations completed per second and is the reciprocal of the time period.
Angular frequency \(\omega\) is defined as \(\omega = 2\pi f\), where \(f\) is the frequency of oscillation.
Phase represents the state of oscillation of a particle at a given instant, determined by the argument of the sine or cosine function.
Phase difference is the difference in phase angles of two oscillatory motions at the same instant.
The general equation of SHM is \(x = A\cos(\omega t + \phi)\), where \(A\) is amplitude and \(\phi\) is phase constant.
Restoring force is the force that always acts towards the mean position and tends to bring the body back to equilibrium.
SHM is called harmonic because its displacement varies sinusoidally with time.
Velocity in SHM is given by \(v = \omega\sqrt{A^2 - x^2}\).
Velocity is maximum at the mean position.
Velocity is zero at the extreme positions.
Acceleration in SHM is given by \(a = -\omega^2 x)\.
Acceleration is maximum at the extreme positions.
Acceleration is zero at the mean position.
Total mechanical energy in SHM is constant and equal to \(\frac{1}{2}kA^2\).
Energy continuously transforms between kinetic and potential forms while total energy remains constant.
Kinetic energy is maximum at the mean position.
Potential energy is maximum at the extreme positions.
It is a mechanical system where a mass attached to a spring executes SHM when displaced from equilibrium.
Hooke’s law states that the restoring force of a spring is proportional to its extension or compression.
The time period is \(T = 2\pi\sqrt{\frac{m}{k}}\).
A simple pendulum consists of a point mass suspended by a light, inextensible string from a fixed support.
A pendulum executes SHM only for small angular displacements.
The time period is \(T = 2\pi\sqrt{\frac{l}{g}}\).
A seconds pendulum has a time period of 2 seconds.
No, the time period of a simple pendulum is independent of the mass of the bob.
For ideal SHM, the time period is independent of amplitude.
It is the distance between the point of suspension and the centre of mass of the bob.
A motion that repeats after equal intervals of time but does not satisfy the SHM condition is periodic but non-SHM.
Motion described by \(x = \sin^2 \omega t\) is periodic but not SHM.
Because it assumes no friction, no energy loss, and perfectly linear restoring forces.
Free oscillations occur when a system oscillates with its natural frequency without external forces.
Damped oscillations are oscillations in which amplitude decreases due to energy loss.
Natural frequency is the frequency with which a system oscillates when disturbed and left free.
SHM can be considered as the projection of uniform circular motion on a diameter.
Pendulum clocks, quartz watches, tuning forks, and spring balances use oscillation principles.
It forms the foundation for waves, sound, AC circuits, and many competitive exam problems.
Numerical problems, derivations, conceptual reasoning, assertion–reason, and graph-based questions.
