Question

Which of the following relations for the displacement of a particle undergoing simple harmonic motion is not correct dimensionally?

• A. $y = a\sin\frac{2\pi t}{T}$
• B. $y = a\cos\omega t$
• C. $y = \frac{a}{T}\sin\left( \frac{t}{a} \right)$
• D. $y = a\sqrt{2}\left( \sin\frac{2\pi t}{T} + \cos\frac{2\pi t}{T} \right)$

Answer 1

Answer: (C)

$y = \frac{a}{T}\sin\left( \frac{t}{a} \right)$

Answer 2

Dimensions on RHS must be displacement [L]. Arguments of sine and cosine should be dimensionless. Hence, option (3) is not correct.