The function $\sin ^{2}(\omega t)$ represents

(D) a simple harmonic motion with a period $\pi / \omega$

(A) a periodic, but not simple harmonic motion with a period $2 \pi / \omega$

(B) a periodic, but not simple harmonic motion with a period $\pi / \omega$

(C) a simple harmonic motion with a period $2 \pi / \omega$

JEE Main · 2005 · 08 May 2005 · Offline · Elasticity & SHM

The function

sin^{2} (ω t)

represents

Answer: (D)

Rewrite

sin^{2} (ω t) = \frac{1 - c o s ( 2 ω t )}{2} = \frac{1}{2} - \frac{1}{2} cos (2 ω t)

. Apart from the constant, this is a cosine oscillation at angular frequency

2 ω

, which is simple harmonic motion with period

T = \frac{2 π}{2 ω} = \frac{π}{ω}

JEE Main · 2005 · 08 May 2005 · Offline · Single correct option