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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