Question

Define Phase of S.H.M ?

Answer 1

Hint:-Phase simply means an angular term which represents the state of a particle in SHM at a certain instant. We calculate the distance of the particle from the mean position during simple harmonic motion and convert it into the angular term that is known as the phase of S.H.M.

Step by step complete solution:-
Definition- The phase of Simple harmonic motion is defined as an angular term which represents the state of a particle from the mean position at a certain instant.
The linear displacement of particle from mean position in simple harmonic motion is represented by sine and cos functions that
Let the general equation of S.H.M. is given by- \[x = A\sin \left( {\omega t + \theta } \right)\]
Here, x = Displacement of particle from mean position at time ‘t’.
 A= Amplitude of S.H.M (Maximum displacement of particle from mean position)
\[\omega \]= Angular frequency ( Rate of change of phase angle per unit time)
t = time
θ = Initial phase at instant ‘t=0’
The quantity $\left( {\omega t + \theta } \right)$is known as phase at instant ‘t’.
Phase difference- If the phase angles of two particles executing S.H.M. are $\left( {\omega t + {\theta _1}} \right)$and $\left( {\omega t + {\theta _2}} \right)$then the phase difference between two particles is given by-
$\vartriangle \phi = \left( {\omega t + {\theta _1}} \right) - \left( {\omega t + {\theta _2}} \right)$
So with the help of this equation we can find the phase difference between two particles executing simple harmonic motion.

Note:-The motion of simple harmonic motion may be linear but the graph of motion is generated with help of phase that is an angular term. We can calculate this one with the help of given parameters and general equation of S.H.M.