# Simple Harmonic Motion

• A body is said to be in SHM if it moves to and fro along a straight line about its mean position such that at any point its acceleration is directly proportional to its displacement in magnitude but opposite in direction and is always directed towards the mean position.
• Phase represents the state of vibration of the particle at any instant of time.
• The difference in the phase angles of two particles in SHM is known as the phase difference between them.
• The starting phase of oscillation is called epoch. If phase is zero y = A sin wt. If phase = \tt \frac{\pi}{2} y = A sin (wt + \tt \frac{\pi}{2})
• Velocity of SHM is given by \tt v = w \sqrt{A^{2} - y^{2}} where w is called angular velocity A = Amplitude and y = displacement of particle.

### View the Topic in this video From 0:21 To 05:23

Disclaimer: Compete.etutor.co may from time to time provide links to third party Internet sites under their respective fair use policy and it may from time to time provide materials from such third parties on this website. These third party sites and any third party materials are provided for viewers convenience and for non-commercial educational purpose only. Compete does not operate or control in any respect any information, products or services available on these third party sites. Compete.etutor.co makes no representations whatsoever concerning the content of these sites and the fact that compete.etutor.co has provided a link to such sites is NOT an endorsement, authorization, sponsorship, or affiliation by compete.etutor.co with respect to such sites, its services, the products displayed, its owners, or its providers.

1. Simple Harmonic Motion (SHM) is that type of oscillatory motion in which the particle moves to and fro about a fixed point. Such that acceleration is proportional to negative of displacement.
The general equation of simple harmonic motion is given by
x(t) = A cos (ωt + Φ)

2. The angular frequency ω is related to the period and frequency of the motion by
\omega = \frac{2 \pi}{T} = 2 \pi \nu

3. The particle velocity and acceleration during SHM as functions of time are given by
\tt v(t) = \frac{d}{dt}x(t) = - \omega A \sin (\omega t + \phi)
\tt a(t) = \frac{d}{dt}v(t) = - \omega^{2} A \cos (\omega t + \phi) = -\omega^{2} x(t)