Question

Can someone pls provide me with a derivation of total energy of a particle executing simple harmonic motion?PLS HELP FRNDS.

Answer 1

total energy of a particle executing shm is TE = 1/2 M(ω)2 A2

=ALWAYS CONSTANT



In simple harmonic motion when a particle is displaced to a position from its mean position, then its kinetic energy gets converted into potential energy and vice-versa. Hence, total energy of a particle remains constant or the total energy in simple harmonic motion does not depend on displacement x.

Kinetic energy = 1/2mv^2 Where V =velocity =w^2(r^2 -y^2)Potential energy =1/2 Ky^2K=spring or force constant Total energy=1/2mw^2r^2Also m w^2 =K Thus expression is 1/2 K r^2


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