At two particular closest instants of time t1 and t2 the displacements of a particle performing SHM are equal. At these instants

If a particle is performing SHM with amplitude A and angular frequency ω and if its initial phase is equal to zero, then its displacement from the mean position will be given by x =A sinωt. Value of sin ωt is same at two different values of the phase. If one is ωt, then the other is (2π−ωt). Hence at these two instants, the phases are unequal. Therefore, option (3) is correct. Velocity of the particle will be equal to ωA2−x2. 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 mean position. Hence (1) is also correct.Since speeds are equal, kinetic energies are also equal. Hence, option (4) is also correct. Acceleration of the particle is a=−ω2x. Since x is same at these two instants, accelerations are also equal. Therefore, option (2) is also correct.