Oscillations - Result Question 30
33. In a simple harmonic motion, when the displacement is one-half the amplitude, what fraction of the total energy is kinetic?
[1996]
(a) 0
(b) $\frac{1}{4}$
(c) $\frac{1}{2}$
(d) $\frac{3}{4}$
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Answer:
Correct Answer: 33. (d)
Solution:
- (d) Total energy of particle executing S.H.M. of amplitude (A).
$E=\frac{1}{2} m \omega^{2} A^{2}$
K.E.of the particle
$=\frac{1}{2} m \omega^{2}(A^{2}-\frac{A^{2}}{4}) \quad(.$ when $.x=\frac{A}{2})$
$=\frac{1}{2} m \omega^{2} \times \frac{3}{4} A^{2}=\frac{1}{2} \times \frac{3}{4} m \omega^{2} A^{2}$
Clearly, $\frac{KE}{\text{ Total Energy }}=\frac{3}{4}$
