Question

Derive an expression for the total energy of a particle executing SHM. Show graphically the variation of P.E. and K.E. with time in SHM.

Answer 1

A particle executing SHM possess two types of energy: 

(i) Potential energy 

(ii) Kinetic energy Potential energy particle of mass m, angular frequency w time t and displacement Y

Answer 2

Total energy in shm

ET = KE + PE = constant

lets assume, at an instance particle is present at mean position and no additional energy is provided to the particle externally.

ET = 1/2 mw²A² + 0;

∵ KE_max = 1/2 mw²A²(at mean position) & PE = 0(at mean position)

ET = 1/2 mw²A² = constant

(this energy remains constant through the motion, assuming medium is ideal)

Energy curve for ideal situation