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Q 01 / 25
An oscillatory motion is always periodic.
Q 02 / 25
Every periodic motion is necessarily oscillatory.
Q 03 / 25
In simple harmonic motion, the restoring force is proportional to displacement from equilibrium.
Q 04 / 25
In SHM, acceleration is maximum at the mean position.
Q 05 / 25
The displacement of a particle executing SHM can be written as \(x = A \sin(\omega t)\).
Q 06 / 25
The velocity of a particle in SHM is maximum at the extreme positions.
Q 07 / 25
The phase of SHM determines the state of motion of the particle at a given instant.
Q 08 / 25
The time period of SHM depends on the amplitude of oscillation.
Q 09 / 25
In SHM, kinetic energy is maximum at the equilibrium position.
Q 10 / 25
The potential energy of a particle executing SHM is zero at extreme positions.
Q 11 / 25
Total mechanical energy remains constant in ideal SHM.
Q 12 / 25
For a spring–mass system, angular frequency is given by \(\omega = \sqrt{\frac{k}{m}}\).
Q 13 / 25
Increasing the mass attached to a spring increases the frequency of oscillation.
Q 14 / 25
The motion of a simple pendulum is strictly SHM for all angles.
Q 15 / 25
The time period of a simple pendulum is \(T = 2\pi\sqrt{\frac{l}{g}}\).
Q 16 / 25
Damping always increases the time period of oscillation.
Q 17 / 25
In damped oscillations, amplitude decreases exponentially with time.
Q 18 / 25
In forced oscillations, resonance occurs when driving frequency equals natural frequency.
Q 19 / 25
The quality factor of an oscillator is a measure of its energy loss per cycle.
Q 20 / 25
Phase difference between displacement and velocity in SHM is \(\frac{\pi}{2}\).
Q 21 / 25
The restoring force in SHM is conservative.
Q 22 / 25
For SHM, total energy is proportional to the square of amplitude.
Q 23 / 25
At a displacement \(x = \frac{A}{\sqrt{2}}\), kinetic and potential energies are equal.
Q 24 / 25
The maximum acceleration in SHM is given by \(a_{\text{max}} = \omega^2 A\).
Q 25 / 25
In SHM, the ratio of maximum kinetic energy to maximum potential energy is always unity.

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.
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