Derive total energy of SHM.
ankitsinghtikkusingh:
here is your answer
How do you calculate the total energy in SHM?
1 ANSWER

Vinod Gohel, former Retired professor of physics at Gujarat University (1962-2003)
Answered Jul 17 2018 · Author has 3.1kanswers and 1.9m answer views
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.
1 ANSWER

Vinod Gohel, former Retired professor of physics at Gujarat University (1962-2003)
Answered Jul 17 2018 · Author has 3.1kanswers and 1.9m answer views
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.
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.
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Heya....❤❤❤
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.
hope it helps...
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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.
hope it helps...
plzz mark me as brainliest my dear !!!
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tysm❤
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Answered by
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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
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
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