A body is performing S.H.M. Then its

(a) Average total energy per cycle is equal to its maximum kinetic energy.

(b) Average kinetic energy per cycle is equal to half of its maximum kinetic energy.

(c) Mean velocity over a complete cycle is equal to 2 π times of its maximum velocity.

(d) Root mean square velocity is 1/√ 2 times of its maximum velocity

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Payal Gupta | Contributor-Level 10

7 months ago

This is a multiple choice answer as classified in NCERT Exemplar

(a, b, d) a) total mechanical energy of the body at any time t is

E= $\frac{1}{2} m$ w²a²

KE=1/2mv²= $\frac{1}{2} m [{\frac{d x}{d t}]}^{2}$

K_max= ½ mw²a²=E

b) K= ½ mw²a²cos²wt

for a cycle value of coswt is =1/2

= 1/4 mw²a²= kmax/2

c) v=dx/dt = a coswt

V_maen =V_max+V_min/2

= aw-aw/2=0

d)V_rms= $\sqrt[]{\frac{v_{1}^{2} + v_{2}^{2}}{2}} = \sqrt[]{\frac{0 + a^{2} w^{2}}{2}} = \frac{a w}{\sqrt[]{2}}$

V_r

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Physics NCERT Exemplar Solutions Class 11th Chapter Fourteen 2025

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