Question

the displacement of a particle along the x -axis is given by x = a sin2omega t. the motion of the particle corresponds to​

Answer 1

Answer:

simple harmonic motion

Explanation:

ok so,

x=A sin(ωt)

differentiating with respect to t (time) we get,

v=Aω cos(ωt)  [dx/dt =v]

again differentiating with respect to t we get

a= -Aω² sin(ωt) [dv/dt = a]

⇒a= -ω² x

⇒a ∝ -x [ω (angular velocity) is a constant]

since acceleration is directly proportional to negative  displacement.

the motion is 'simple harmonic motion'