Oscillations

JEE Main level, single correct, medium

87 of 194

Question 87 of 194

For a body executing S.H.M. :
(a) Potential energy is always equal to its K.E.K.E.
(b) Average potential and kinetic energy over any given time interval are always equal.
(c) Sum of the kinetic and potential energy at any point of time is constant.
(d) Average K.E.K.E. in one time period is equal to average potential energy in one time period.
Choose the most appropriate option from the options given below :

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Answer: (A) (c) and (d)

The formula of kinetic energy in S.H.M. is, K.E.=12mω2(A2−x2)2K.E.=\dfrac{1}{2}m{\omega }^{2}{\left(\sqrt{{A}^{2}-{x}^{2}}\right)}^{2}, where AA is the amplitude of the S.H.M. the formula of potential energy is, P.E.=12mω2x2P.E.=\dfrac{1}{2}m{\omega }^{2}{x}^{2}, so the net energy is defined as, T.E.=P.E.+K.E.=12mω2A2T.E.=P.E.+K.E.=\dfrac{1}{2}m{\omega }^{2}{A}^{2} so the total energy is always constant. Since, energy changes from potential to kinetic and vice-versa the average K.E.K.E. in one time period is equal to the average P.E.P.E. in one time period.

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