A body of mass ' m ' performs linear S.H.M. given by equation x = P sin ω t + Q sin ( ω t + 2 π ) . The total energy of the particle at any instant is

x = P sin ω t + Q sin ( ω t + 2 π ) It can be considered as composition of two S.H.M. of amplitudes P and Q having phase difference 2 π . ∴ Resultant amplitude R = P 2 + Q 2 Total energy E = 2 1 m ω 2 R 2 = 2 1 m ω 2 ( P 2 + Q 2 )

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PhysicsSHMEnergyMedium2 minPYQ_2021

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A body of mass ' $m$ ' performs linear S.H.M. given by equation $x = P sin ω t + Q sin (ω t + \frac{π}{2})$ . The total energy of the particle at any instant is

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$x = P sin ω t + Q sin (ω t + \frac{π}{2})$ It can be considered as composition of two S.H.M. of amplitudes $P$ and $Q$ having phase difference $\frac{π}{2}$ . $∴$ Resultant amplitude $R = P^{2} + Q^{2}$ Total energy $E = \frac{1}{2} m ω^{2} R^{2}$ $= \frac{1}{2} m ω^{2} (P^{2} + Q^{2})$

Stream:MHT_CETSubject:PhysicsTopic:SHMSubtopic:Energy

⏱ 2mℹ️ Source: PYQ_2021

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