SHMHard
Question
The displacement of a particle along the x axis is given by x = a sin2 ωt . The motion of the particle corresponds to
Options
A.simple harmonic motion of frequency ω/π
B.simple harmonic motion of frequency 3ω/2π
C.non simple harmonic motion
D.simple harmonic motion of frequency ω/2π
Solution
x = a sin2 ωt
= a
(∵ cos2θ = 1 - 2 sin2θ)
∴ Velocity, v =
= ω2a sin2ωt
Acceleration, a =
= 2ω2 a cos2ωt
For the given displacement x = a sin2ωt
a ∝ - x is not satisfied.
Hence, the motion of the particle is non simple harmonic motion.
Note : The given motion is a periodic motion with a time period T =
= a
(∵ cos2θ = 1 - 2 sin2θ)∴ Velocity, v =
= ω2a sin2ωtAcceleration, a =
= 2ω2 a cos2ωtFor the given displacement x = a sin2ωt
a ∝ - x is not satisfied.
Hence, the motion of the particle is non simple harmonic motion.
Note : The given motion is a periodic motion with a time period T =
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