Simple Harmonic Motion and Oscillations

Vocabulary flashcards based on Topic 5.3 of the OCR Physics Year 2 Textbook covering Simple Harmonic Motion, its defining equations, graphical analysis, energy interchanges, damping types, and resonance.

Displacement ($x$)

The distance an object moves from its equilibrium (or rest) position; may be positive or negative.

Amplitude ($x_0$)

The maximum displacement of an oscillating body from its equilibrium position; it is always positive.

Frequency ($f$)

The number of oscillations per unit time at any point, measured in hertz ($\text{Hz}$).

Period ($T$)

The time taken for one complete pattern of oscillation at any point, measured in seconds ($\text{s}$).

Angular frequency ($\omega$)

The rate of change of phase, calculated as $\omega = 2\times \frac{\pi}{T}$ or $\omega = 2\pi f$, expressed in radians per second ($\text{rad}\,\text{s}^{-1}$).

Phase difference ($\phi$)

The fraction of a complete cycle or oscillation between two oscillating points, expressed in degrees or radians.

Simple harmonic motion (s.h.m.)

Oscillatory motion in which the acceleration of a body is directly proportional to its displacement from a fixed point and always directed towards that fixed point.

In phase

Two points on an oscillating or vibrating body that are at exactly the same stage of their oscillation, having zero phase difference.

Antiphase

The condition where two points on an oscillating body move in opposite directions to one another.

Defining equation of simple harmonic motion

The mathematical relationship $a = -\omega^2 x$ or $a = -(2\pi f)^2 x$, showing acceleration is proportional and opposite in direction to displacement.

Velocity in simple harmonic motion

The rate of change of displacement given by $v = \pm \omega \sqrt{A^2 - x^2}$, where $A$ is amplitude and $x$ is displacement.

Maximum acceleration ($a_{\text{max}}$)

The maximum acceleration experienced by an oscillating body at its maximum displacement ($x = A$), defined as $a_{\text{max}} = \omega^2 A$.

Maximum velocity ($v_{\text{max}}$)

The maximum speed of an oscillator as it passes through its equilibrium position ($x = 0$), defined as $v_{\text{max}} = \omega A$.

Isochronous oscillator

An oscillator whose time period is constant and completely independent of the amplitude of oscillation.

Damping forces

Forces that reduce the amplitude of an oscillation over time by removing energy from the oscillating system.

Natural damping

Damping that occurs naturally due to air resistance or other inherent frictional forces resisting motion.

Artificial damping

The deliberate introduction of resistive forces to reduce vibration amplitude quickly and prevent damage or discomfort.

Light damping

Damping in which the time period of oscillation remains almost unchanged, but the amplitude gradually decreases over time.

Heavy damping

Damping where resistive forces are so large that no oscillation occurs, and the system slowly returns to its equilibrium position.

Critical damping

The cross-over boundary state between oscillation and no oscillation, returning the system to equilibrium in the shortest possible time without oscillating.

Free oscillations

Oscillations that occur when a system is displaced and allowed to oscillate without any external, periodic driving force.

Natural frequency

The specific frequency at which a system oscillates when undergoing free oscillations.

Forced oscillations

Oscillations that occur when a system is subjected to a continuous external periodic driving force.

Driving frequency

The frequency of the external force applied to a system undergoing forced oscillations.

Resonance

The phenomenon occurring in forced oscillations when the driving frequency equals the natural frequency of the driven system, producing maximum amplitude oscillations.

Barton's pendulums

An experimental demonstration of resonance where a heavy driver pendulum transfers energy along a string to set other pendulums in motion, causing maximum amplitude in the driven pendulum of equal length.