A particle executes SHM period of 8 seconds After what
| A particle executes S.H.M. period of 8 seconds. After what time of its passing through the mean position will the energy be half kinetic and half potential?
A. 1s
B. 2s
C. 3s
D. 4s
Please scroll down to see the correct answer and solution guide.
Right Answer is: A
SOLUTION
ω=2π8=π4rads−1
Let 't' be the time after which the energy will be half kinetic and half potential.
Since motion starts from mean position, y=Asinωt
dydt=v=Acosωt.ω
K.E=12mv2=12m.A2ω2cos2ωt. This must be half of the total energy.
∴12mA2ω2cos2ωt=12.12mω2A2
∴cosωt=1√2;ωt=π4;t=π4.ω=(π4)(4π)=1s.