Question

Does S.H.M obey law of conservation of energy?​

Answer 1

Answer:

YES

Explanation:

In simple harmonic motion, there is a continuous interchange of kinetic energy and potential energy. If mechanical energy is conserved the sum of the kinetic energy and potential energy should be constant at all times during the oscillation.

Answer 2

Yes, particles in SHM follow the Law of Conservation of Mechanical Energy.

• Let's assume that an object of mass 'm' is in SHM with amplitude 'a' and angular frequency $\omega$.

So, at a point x from mean point :

$1) \: KE = \dfrac{1}{2} m { \omega}^{2} ( {a}^{2} - {x}^{2} )$

$2) \: PE= \dfrac{1}{2} m { \omega}^{2} {x}^{2}$

• So, total energy will be :

$TE=KE + PE$

$\implies TE= \dfrac{1}{2} m { \omega}^{2} ( {a}^{2} - {x}^{2} + {x}^{2} )$

$\implies TE= \dfrac{1}{2} m { \omega}^{2} {a}^{2}$

$\implies TE= constant$

• The KE and PE varies depending on the position of the particle, but total energy always remains conserved.

So, the total energy in SHM always remains constant and hence conserved.