Prove that the average kinetic/pitential energy have 2 times of frequency of SHM
Answers
Answered by
1
In SHM the velocity is given by
v(t)=dx/dt=−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 12mv^2 which is given by
K(t)=12mv^2(t)
=12mω^2A^2sin^2(ωt+φ))
Now the time period of K.E is nothing but the time period of sin^2 (ωt) which is π/ω.
Frequency of any function is inverse of time period so
frequency of K.E. = ω/π
frequency of velocity v(t)= ω/2π
that is frequency of kinetic energy is double than that of the velocity.
v(t)=dx/dt=−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 12mv^2 which is given by
K(t)=12mv^2(t)
=12mω^2A^2sin^2(ωt+φ))
Now the time period of K.E is nothing but the time period of sin^2 (ωt) which is π/ω.
Frequency of any function is inverse of time period so
frequency of K.E. = ω/π
frequency of velocity v(t)= ω/2π
that is frequency of kinetic energy is double than that of the velocity.
Similar questions