Question Detail
Question
When the displacement of a body oscillating on a spring is half its amplitude (x = A/2), what fraction of its total energy is its kinetic energy?
Correct Answer
Option C is the correct answer.
Detailed Explanation
From Worked Example 40 (page 43), the total mechanical energy is E_T = ½kA². The potential energy at displacement x is P.E = ½kx². When x = A/2, P.E = ½k(A/2)² = ½k(A²/4) = (1/4)E_T. Since E_T = K.E + P.E, then K.E = E_T - P.E = E_T - (1/4)E_T = (3/4)E_T. Therefore, the kinetic energy is 3/4 of the total energy.
Hint
Recall the formulas for total energy (E_T), potential energy (P.E), and kinetic energy (K.E) in SHM. Use the conservation of energy (E_T = P.E + K.E).