Question

A particle moves on the X-axis according to the equation $x=A+Bsin\omega t$. The motion is simple harmonic with amplitude.

• A. A
• B. B
• C. A+B
• D. $\sqrt{A^2+B^2}$

Answer 1

The correct option is B B

We are given $x=A+Bsin\omega t$

We can see that the second term basically is the equation of an SHM with amplitude B. What's the first term doing there? Let's think about it. If it were just B sin ωt, it would be an SHM about the origin. Adding a constant to this entire thing would just shift the mean position from origin to x = A. Now the particle is doing SHM about x = A with an amplitude of B. Yes B! because amplitude is how far the particle goes from the mean position. The new means position is x = A but the particle's max displacement is still B from it!