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Time period of a simple pendulum is 2s and it can go to and fro from equilibrium position at a maximum distance of 6cm. If at the start of the motion the pendulum is in the position of maximum displacement towards the right of the equilibrium position, then write the displacement equation of the pendulum. |
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Answer» Here, `T=2s, A=6cm, ` `omega=(2pi)/(T)=(2pi)/(2pirad//s` Let `phi_(0)` be the initial phase of the pendulum, then displacement of particle executing SHM at time t is given by `y=Asin(omegat+phi_(0))=Asin((2pi)/(T)t+phi_(0))` `y=6sin((2pi)/(2)t+phi_(0))=6sin(pit+phi_(0))` when `t=0,y=6cm,` so `6=6sin(pixx0+phi_(0))=6sinphi_(0)` or `sinphi_(0)=1=sinpi//2or phi_(0)=(pi//2)rad` Hence displacement equation for the simple pendulum is `y=6sin(pit+pi//2)=6cospit` |
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