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7.2 S.H.M. & U.C.M.

Figure 2

Consider a particle performing U.C.M. on a circle whose center is `O' and radius is `r'. Let Q be the uniform angular velocity in U.C.M. Consider projection `Q' of instantaneous position `P' on a horizontal diagonal AB. The motion of the particle at `Q' as `P' moves on circle is easily seen to be S.H.M.

Thus projection of U.C.M. on any diagonal is S.H.M.

Displacement in S.H.M.

Let the particle in U.C.M. be at an instantaneous position P at t = 0 sec. Let it move to P' in t sec.

Then the displacement x (always to be measured from mean position in S.H.M.) is given by,

Velocity in S.H.M.

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7.1 Linear Simple Harmonic Motion
7.2 S.H.M. & U.C.M.
7.3 Simple Pendulum
7.4 Energy in S.H.M.

Chapter 8

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