A particle starts SHM at time t = 0. Its amplitude is A and angular frequency is ω. At time t = 0 its kinetic energy is E4 , where E is total energy. Assuming potential energy to be zero at mean position, the displacement-time equation of the particle can be written as

If the equation of SHM is x=A cos ωt+φ, KE at t=o is equal to Esin2φ=E4⇒φ=π6,-π6If the equation of SHM is x=A sin(ωt+φ), KE at t=0 is equal to Ecos2φ=E4⇒φ=π3,-2π3

A particle starts SHM at time t = 0. Its amplitude is A and angular frequency is ω. At time t = 0 its kinetic energy is E4 , where E is total energy. Assuming potential energy to be zero at mean position, the displacement-time equation of the particle can be written as

If the equation of SHM is x=A cos ωt+φ, KE at t=o is equal to Esin2φ=E4⇒φ=π6,-π6If the equation of SHM is x=A sin(ωt+φ), KE at t=0 is equal to Ecos2φ=E4⇒φ=π3,-2π3

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A particle starts SHM at time t = 0. Its amplitude is A and angular frequency is $ω$ . At time t = 0 its kinetic energy is $\frac{E}{4}$ , where E is total energy. Assuming potential energy to be zero at mean position, the displacement-time equation of the particle can be written as

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$x = Asin (ωt - \frac{2 π}{3})$

$x = Acos (ωt - \frac{π}{6})$

$x = Asin (ωt + \frac{π}{3})$

$x = Acos (ωt + \frac{π}{6})$

answer is A, B, C, D.

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Detailed Solution

If the equation of SHM is x=A cos $(ω t + φ), K E a t t = o i s e q u a l t o E \sin^{2} φ = \frac{E}{4} \Rightarrow φ = \frac{π}{6}, - \frac{π}{6}$

If the equation of SHM is x=A sin( $ω t + φ), K E a t t = 0 i s e q u a l t o E \cos^{2} φ = \frac{E}{4} \Rightarrow φ = \frac{π}{3}, - \frac{2 π}{3}$