For Velocity and Acceleration of a Particle Moving With Simple Harmonic Motion (SHM), consider a particle, moving round the circumference of a circle of radius r, with a uniform angular velocity ω rad/s, as shown in Fig. 1.32. Let *P* be any position of the particle after t seconds and θ be the angle turned by the particle in t seconds. We know that

θ = ω.t, and x = rcosθ = rcosωt

The velocity of N (which is the projection of *P* on *XX’*) is the component of the velocity of *P*parallel to *XX’*.

VN = v sinθ = ω.rsinθ

The velocity is maximum, when x = 0, i.e. when *N* passes through O (i.e. mean position).

v*max* = ω.r

The acceleration of *N *is the component of the acceleration of P parallel to *XX’* and is directed

towards the center O.

The acceleration is maximum, when x = r, i.e. when P is at *X or X’*.

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