Question

Relation between frequecy of displacement and kinetic energy in shm

Answer 1

Answer:

Explanation: In SHM the velocity is given by

v(t)=dxdt=−Aωsin(ωt+φ),

The time period of v(t) is nothing but the time period of sin(ωt) function which is 2π/ω.

Now the K.E is 12mv2 which is given by K(t)=12mv2(t)=12mω2A2sin2(ωt+φ))

Now the time period of K.E is nothing but the time period of sin2(ωt) which is π/ω.

Frequency of any function is inverse of time period so

frequency of K.E = ωπ

and frequency of velocity v(t) = ω2π

,that is frequency of kinetic energy is double than that of the velocity.