Question

A body executes simple harmonic motion. The potential energy (P.E.), the kinetic energy(K.E.) and total energy (T.E.) are measured as function of displacement x. Which of the following statement is true?

• A. K.E. is maximum when x = 0
• B. T.E. is zero when x = 0
• C. K.E. is maximum when x is maximum
• D. P.E. is maximum when x = 0.

Answer 1

The correct option is A K.E. is maximum when x = 0

Energies of body of mass $m$ executing $SHM$ are given as-

Potential energy $P.E=\frac{1}{2}m{w}^2{x}^2$

Kinetic energy $K.E=\frac{1}{2}m{w}^2(A^2-x^2)$

Total energy $T.E=\frac{1}{2}m{w}^2{A}^2$

Conclusions:

P.E is minimum when $x=0$

Also, K.E is maximum where $x$ is minimum i.e at $x=0$

T.E is constant but never equals to zero.