Question

The displacement of a particle is represented by the equation y = sin3 $\omega$t. The motion is

• A. Non-periodic
• B. Periodic but not simple harmonic
• C. Simple harmonic with period 2$\pi$ /$\omega$
• D. Simple harmonic with period $\pi$ /$\omega$.

Answer 1

Answer: (B)

Periodic but not simple harmonic

Answer 2

AS

$\sin^{3}\omega t = (\sin\omega t)^{3} = \lbrack\sin(\omega t + 2\pi)\rbrack^{3} = \lbrack\sin\omega(t + 2\pi/\omega)\rbrack^{3}y = \sin^{3}\omega t$ represent a periodic motion with period $2\pi/\omega$ further as $d^{2}y/dt^{2}$ is not $\propto ( - y)$ the function does not represent SHM.