NEET Physics: Waves – NCERT Masterclass & 100 MCQ Quiz

OSCILLATIONS & SHM

Complete NCERT Study Notes & 5-Part Mega Quiz for NEET

1. Periodic and Oscillatory Motions

Periodic Motion: A motion that repeats itself at regular intervals of time (e.g., planets revolving around the sun).
Oscillatory Motion: A to-and-fro motion about a fixed mean position (e.g., a swinging pendulum). Every oscillatory motion is periodic, but every periodic motion is not necessarily oscillatory.

Time Period ($T$): The smallest interval of time after which the motion is repeated.
Frequency ($\nu$ or $f$): The number of oscillations completed per unit time. $f = \frac{1}{T}$. Angular frequency $\omega = 2\pi f = \frac{2\pi}{T}$.

2. Simple Harmonic Motion (SHM)

SHM is the simplest form of oscillatory motion. A particle executes SHM if the restoring force acting on it is directly proportional to its displacement from the mean position and is always directed towards the mean position.

$$F = -kx \implies a = -\omega^2 x$$

Where $k$ is the force constant, and $\omega = \sqrt{\frac{k}{m}}$.

3. Kinematics of SHM

The displacement of a particle in SHM at any time $t$ is given by:

$$x(t) = A \cos(\omega t + \phi)$$

• Amplitude ($A$): Maximum displacement from the mean position.
• Phase ($\omega t + \phi$): Defines the state of motion (position and direction) at any instant.
• Velocity ($v$): $v = \frac{dx}{dt} = -\omega A \sin(\omega t + \phi) = \pm \omega \sqrt{A^2 - x^2}$
• Acceleration ($a$): $a = \frac{dv}{dt} = -\omega^2 A \cos(\omega t + \phi) = -\omega^2 x$

4. Energy in Simple Harmonic Motion

In the absence of dissipative forces, the total mechanical energy of a particle in SHM remains perfectly constant.

• Potential Energy ($U$): $U = \frac{1}{2} k x^2 = \frac{1}{2} m \omega^2 x^2$
• Kinetic Energy ($K$): $K = \frac{1}{2} m v^2 = \frac{1}{2} m \omega^2 (A^2 - x^2)$
• Total Energy ($E$): $E = K + U = \frac{1}{2} m \omega^2 A^2$ (Constant)

5. The Simple Pendulum & Springs

Spring-Mass System: Time period $T = 2\pi \sqrt{\frac{m}{k}}$.

• Springs in Series: $\frac{1}{k_{eq}} = \frac{1}{k_1} + \frac{1}{k_2}$
• Springs in Parallel: $k_{eq} = k_1 + k_2$

Simple Pendulum: A heavy point mass suspended by a massless, inextensible string. For small angles of swing, it executes SHM.

$$T = 2\pi \sqrt{\frac{L}{g}}$$

Note: The time period of a simple pendulum is totally independent of the mass of the bob.

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🚀 NEET OSCILLATIONS MEGA QUIZ (100 MCQ)

Solve the 5 parts below to master SHM Equations, Energy, and Pendulums.

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