Simple Harmonic Motion (SHM)

The motion that repeats itself after regular intervals of time is called periodic motion. If a particle in the periodic motion moves to and fro over the same path, the motion is said to be vibrating or oscillating.

Equilibrium Position: The point at which no net force acts on the oscillating body is known as equilibrium position or mean position.

• Displacement of the body is minimum.
• Velocity of the body is maximum.
• Acceleration of the body is minimum.
• PE of the body is minimum.
• KE of the body is maximum.

Extreme Position: The point at which maximum force acts on the oscillating body is known as Extreme Position.

If a particle moves along a straight line with its acceleration directed towards a fixed point in its path and the magnitude of the acceleration is directly proportional to the displacement from its equilibrium position, then it is said to be in simple harmonic motion. 

If the to and fro motion is along a straight line it is called linear SHM. If the displacement is measured in terms of angles then it is called angular SHM.

The time taken for one complete vibration or oscillation is called time period (T). The number of oscillations or vibrations made per second is called frequency (n). The maximum displacement of the particle measured from the equilibrium position is called amplitude. 

Phase: Phase at any instant gives the state of the vibrating particle with respect to time in a specified direction with reference to a fixed point (mean position).

If the phase is zero, the particle is crossing the mean position. If the phase is π/2, the particle is at the extreme position. The initial phase at t = 0 of a particle in SHM is called phase constant.

Representation of SHM

The simple harmonic motion is represented as

Y = A sin(ωt + φ)

Velocity: The rate of change of displacement is called velocity.

v = dy/dt = Aω cos(ωt + φ)