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A body executes simple harmonic motion. The potential energy (P.E.), the kinetic energy (K.E.) and total energy (T.E.) are measured as a function of time t. Which of the following statements is true. Assume that the particle started at \( t=0 \) at its mean position

1. P.E. is maximum when \( t=0 \)
2. T.E. is zero when \( t=0 \)
3. K.E. is maximum when \( t=0 \)
4. K.E. is minimum when t =

Correct answer: K.E. is minimum when t =

Solution

In simple harmonic motion, the mean position has zero displacement, so the potential energy is minimum there. Since total energy stays constant, the kinetic energy must be maximum at that instant; therefore the minimum kinetic energy occurs a quarter period later, when the particle reaches an extreme position.

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