A particle of mass m executes simple harmonic motion with amplitude a and frequency v. The average kinetic energy during its motion from the position of equilinrium to the end is.A. (a) `2pi^(2)ma^(2)v^(2)`B. (b) `pi^(2)ma^(2)v^(2)`C. (c ) `1/2ma^(2)v^(2)`D. (d) `4pi^(2)ma^(2)v^(2)`

A particle of mass m executes simple harmonic motion with amplitude a

1.	A particle of mass m executes simple harmonic motion with amplitude a and frequency v. The average kinetic energy during its motion from the position of equilinrium to the end is.A. (a) `2pi^(2)ma^(2)v^(2)`B. (b) `pi^(2)ma^(2)v^(2)`C. (c ) `1/2ma^(2)v^(2)`D. (d) `4pi^(2)ma^(2)v^(2)`
Answer» Correct Answer - B (b) KEY CONCEPT: The instantaneous kinetic energy of a particle executing S.H.M. is given by. `K=1/2ma^(2) omega^(2) sin^(2)omegat` :. Average K.E. `=ltKgelt1/2momega^(2)a^(2) sin^(2)omegatgt` `=1/2momega^(2)a^(2)ltsin^(2)omegatgt` `=1/2momega^(2)a^(2)(1/2) (:. ltsin^(2)thetage1/2)` `=1/2momega^(2)a^(2)=1/2ma^(2)(2piv)^(2) (:. omega=2piv)` `=1/2momega^(2)a^(2) =1/2ma^(2) (2piv)^2) (:. omegapiv)` or, `ltKgtpi^(2)ma^(2)v^(2)`.

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A particle of mass m executes simple harmonic motion with amplitude a and frequency v. The average kinetic energy during its motion from the position of equilinrium to the end is.A. (a) `2pi^(2)ma^(2)v^(2)`B. (b) `pi^(2)ma^(2)v^(2)`C. (c ) `1/2ma^(2)v^(2)`D. (d) `4pi^(2)ma^(2)v^(2)`

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