Question

At two particular closest instant of time `t_1` and `t_2` the displacements of a particle performing SHM are equal. At these instant
A. instantaneaous speed are equal
B. instantaneous acceleration are equal
C. phase of the motion are unequal
D. kinetic energies are equal

Answer 1

Correct Answer - A::B::C::D
If a particle is performing SHM with amplitude A and angular frequency `omega` and if its initial phase is equal to zero, then its displacement from the mean position will be given by `x=Asinomegat`.
Value of `sinomegat` is same at two different values of the phase. If one is `omegat` then the other is `(pi-omegat)`. Hence at these two instant, the phases are unequal. Therefore, option (c ) is correct.
Velocity of the particle will be equal to `omegasqrt((A^2-x^2))`. Since x is same at these two instants, therefore the magnitude of velocity will be same or the speeds are equal. However, velocities are unequal because at one instant direction of motion of the particle will be towards the extreme position or away from mean position and at the other instant, it will be towards the me3an position. Hence (a) is also correct.
Since speeds are equal, kinetic energies are also equal. Hence. option (d) is also correct. Acceleration of the particle is `a=-omega^2x`. Since x is same at these two instant, accelerations are also equal. Therefore, option (b) is also correct.