Question

The amplitude of a particle executing SHM about $O$ is $10\, cm$. Then:

• A. When the K.E. is 0.64 of its maximum K.E. its displacement is 6 cm from O.
• B. When the displacement is 5 cm from O its K.E. is 0.75 times its maximum K.E.
• C. Its total energy of SHM at any point is equal to its maximum K.E if at mean position potential energy is zero
• D. Its speed is half the maximum speed when its displacement is half the maximum displacement.

Answer 1

Answer: (A), (B), (C)

At $KE \,0.64$ times that of maximum $KE$ the velocity would be $0.8$ times that of maximum velocity, now we can use the relation of velocity and displacement $v=\left[(k / m)\left(A^{2}-x^{2}\right)\right]^{1 / 2}$ to verify that options $(A)$ and $(B)$ are correct.