Question

Derive total energy of SHM.

Answer 1

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here is ur answer...

Total Energy in Simple Harmonic Motion (T.E.) The total energy in simple harmonic motion is the sum of its potential energy and kinetic energy. ... As ω2 , a2 are constants, the total energy in the simple harmonic motion of a particle performing simple harmonic motion remains constant.

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Answer 2

HI RAGAVI your answer
Total energy in SHM is

E=Kinetic energy,K + Potential energy,U.

Now, K=(1/2) mv^2………..(1)

m is mass of particle and v is it's velocity when it's displacement is , say , y. We have considered SHM along y- axis with y=0 as equilibrium position.

Let A be the amplitude. Then,

v^2= w^A^2 - w^2y^2. ( from expression for velocity in SHM ).Therefore,

K= (1/2) m ( w^2A^2 - w^2y^2)……….(2).

But, (1/2)mw^2y^2 = (1/2)ky^2, where k is force constant .

Now, U= (1/2)ky^2. Using this expression in equation (2),

K=(1/2)mw^2A^2-U OR

Total energy, E=K+U=(1/2)mw^2A^2 OR

E= (1/2)kA^2.
HOPE THIS WILL HELP U