Question

Which of the following relations for the displacement of a particle undergoing simple harmonic motion is not correct dimensionally? In the relations given, y is displacement, a is amplitude, t is time and T is time period.

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

Answer 1

The correct option is C $y=\frac{a}{T}sin\left(\frac{t}{a}\right)$

Dimensions on RHS must be displacement [L]. Arguments of sine and cosine should be dimensionless.