Oscillation and Simple Harmonic Motion

Vocabulary flashcards covering the fundamental concepts of periodic motion, oscillatory motion, Simple Harmonic Motion (SHM), and the principles of resonance.

Periodic Motion

A motion that repeats after a definite, regular, or fixed interval of time.

Oscillatory Motion

A type of motion where an object moves back and forth in opposite directions repeatedly around a fixed central position at regular intervals.

Simple Harmonic Motion (SHM)

A motion where a particle moves to and fro in a straight line about an equilibrium position such that the force acting upon it is always directly proportional to its displacement and directed towards the mean position.

Restoring Force

A force that is directly proportional to the displacement from the mean position and directed opposite to it, expressed by the equation $F = -kx$.

Amplitude

The maximum displacement from the equilibrium position during oscillation.

Period (T)

The time taken for a particle to make one complete oscillation, cycle, or rotation.

Frequency (f)

The number of oscillations completed in one second for a particle executing SHM, defined as $f = \frac{1}{T}$.

Angular Frequency (\omega)

The angular rate of motion in SHM, related to frequency and period by the formulas $\omega = 2\pi f$ and \omega = \frac{2\text{\pi}}{T}.

Mean Position

The central point or equilibrium position around which an object oscillates; at this point, displacement is zero and velocity is maximum ($v_{max} = \omega A$).

Extreme Position

The points of maximum displacement in SHM where velocity is $0$ and acceleration is maximum ($a_{max} = \omega^2 A$).

Potential Energy (PE) in SHM

Energy associated with the restoring force, given by $PE = \frac{1}{2} kx^2$; it is maximum at the extreme positions.

Kinetic Energy (KE) in SHM

Energy based on the motion of the mass, given by $KE = \frac{1}{2} m v^2$ or $KE = \frac{1}{2} k(A^2 - x^2)$; it is maximum at the mean position.

Total Energy (TE) in SHM

The sum of kinetic and potential energy, which remains constant according to the law of conservation of energy and is equal to $TE = \frac{1}{2} kA^2$.

Time Period of a Simple Pendulum

The time for one complete oscillation of a pendulum, determined by the formula $T = 2\pi \sqrt{\frac{L}{g}}$, where $L$ is the length and $g$ is acceleration due to gravity.

Time Period of Horizontal SHM

The time for one cycle of a mass on a spring, calculated as $T = 2\pi \sqrt{\frac{m}{k}}$ where $m$ is mass and $k$ is the spring constant.

Free Oscillation

Oscillation that occurs with no transfer of energy to or from the surroundings, maintaining a constant amplitude and frequency (natural frequency).

Natural Frequency

The frequency of free oscillation of a system after a disturbance, determined by the system's properties like shape, size, and material.

Forced Vibration (Driven Oscillation)

Oscillation that occurs when an external periodic driving force is applied to a system.

Driving Frequency

The rate at which an object vibrates due to an external force.

Resonance

The phenomenon where the amplitude of oscillation increases significantly because the driving frequency is very close to the natural frequency of the body.