Oscillations Test - 2

It executes simple harmonic motion because in this motion restoring force is directly proportional to the displacement towards the mean position at any time.

In oscillatory motion object moves to and fro about mean position periodically or after a particular interval of time.All oscillatory motions are periodic in nature.

A motion of a body that repeats itself at regular intervals of time on the same path like rotation of earth around sun in 365.25 days

Time period of an oscillatory motion is the smallest interval of time for one complete oscillation.As when we apply the force on the bob,bob moves from mean position to extreme position then form extreme position to mean position and then again from mean to extreme in opposite direction and at last come to mean position.The time taken by bob in this whole process is called period of oscillation.

Frequency is defined as number of oscillation completed by an oscillating body in unit time i.e. in one second during oscillatory motion.

  ν = 1/T

Because sine and cosine functions both are periodic in nature and according to Fourier theorem a" Fourier series" is a way to represent a function as the sum of simple sine waves. More formally, it decomposes any periodic function or periodic signal into the sum of a (possibly infinite) set of simple oscillating functions, namely sines and cosines, or in simple terms any periodic function can be expressed as sum or superposition of sine and cosine functions with fixed time periods.

Equation of simple harmonic motion is given by

x(t) = Acos( ωt + ϕ )

Where x(t) is the displacement of body at any instant of time

A is the amplitude of the body

( ωt + ϕ ) is the phase angle at the instant of time.