The displacement of a particle along the x-axis is given by x = a sin² ωt. The motion of the particle corresponds to

simple of harmonic motion of frequency ω/π

simple harmonic motion of frequency 3ω/2π

non simple harmonic motion

simple harmonic motion of frequency ω/2π

Solution

simple harmonic motion of frequency ω/2π

For space straight a space particle space executing space SHM acceleration space left parenthesis straight a right parenthesis space proportional to space minus straight omega squared space displacement space left parenthesis straight x right parenthesis space.... space left parenthesis straight i right parenthesis space Given space straight x space equals space straight a space sin squared space ωt space space space..... space left parenthesis ii right parenthesis Differentiating space the space above space equation space straight w. straight r. straight t space we space get dx over dt space equals 2 aω left parenthesis space sin space ωt right parenthesis left parenthesis cost space ωt right parenthesis Again space differentiating comma space we space get fraction numerator straight d squared straight x over denominator dt squared end fraction space equals space straight a space equals space 2 aω squared space left square bracket space cos squared space ωt minus space sin space ωt right square bracket equals space 2 aω squared space cos space 2 ωt

The given equation does not satisfy the condition for SHM (Eq. (i) ]. Therefore, motion is not simple harmonic.

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