Question

n=1/2π √g/l where n is frequency, g is acceleration due to gravity and l is length

Answer 1

Periodic Motion

A motion which repeats itself identically after a fixed interval of time is called periodic motion. e.g., orbital motion of the earth around the sun, motion of arms of a clock, motion of a simple pendulum etc.

Oscillatory Motion

A periodic motion taking place to and fro or back and forth about a fixed point, is called oscillatory motion, e.g., motion of a simple pendulum, motion of a loaded spring etc.

Note Every oscillatory motion is periodic motion but every periodic motion is not oscillatory motion.

Harmonic Oscillation

The oscillation which can be expressed in terms of single harmonic function, i.e., sine or cosine function, is called harmonic oscillation.

Simple Harmonic Motion

A harmonic oscillation of constant amplitude and of single frequency under a restoring force whose magnitude is proportional to the displacement and always acts towards mean Position is called Simple Harmonic Motion (SHM).



A simple harmonic oscillation can be expressed as

y = a sin ωt

or y = a cos ωt

Where a = amplitude of oscillation.

Non-harmonic Oscillation

A non-harmonic oscillation is a combination of two or more than two harmonic oscillations.

It can be expressed as y = a sin ωt + b sin 2ωt

Some Terms Related to SHM

(i) Time Period Time taken by the body to complete one oscillation is known as time period. It is denoted by T.

(ii) Frequency The number of oscillations completed by the body in one second is called frequency. It is denoted by v.

Its SI unit is ‘hertz’ or ‘second-1‘.

Frequency = 1 / Time period

(iii) Angular Frequency The product of frequency with factor 2π is called angular frequency. It is denoted by ω.

Angular frequency (ω) = 2πv

Its SI unit is ‘hertz’ or ‘second-1‘.

(iv) Displacement A physical quantity which changes uniformly with time in a periodic motion. is called displacement. It is denoted by y.

(v) Amplitude The maximum displacement in any direction from mean position is called amplitude. It is denoted by a.

(vi) Phase A physical quantity which express the position and direction of motion of an oscillating particle, is called phase. It is denoted by φ.

Simple harmonic motion is defined as the projection of a uniform circular motion on any diameter of a circle of reference.