Question

A particle moves on the X-axis according to the equation x = A + B sin ωt. The motion is simple harmonic with amplitude
(a) A
(b) B
(c) A + B
(d) √A2+B2.

Answer 1

Given equation is

Y=A+Bsin(wt)

Y-A=Bsin(wt)------(1)

Comparing equation no. 1 with the equation of simple harmonic motion

Y=Tsin(wt+Φ)

here we get, T=B

So, amplitude is B

Hence from the given options, option(b) is correct.

Answer 2

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

Explanation:

According to the equation, $x=A+B \sin \omega t$,  

Displacement x0 at t = 0 is shown as $x 0=\sin \omega(0)+A=A$

When sinωt, the displacement x will be maximum and is 1

or,

$x \mathrm{m}=\mathrm{B}+\mathrm{A}$

Then, the amplitude will be xm

$-x o=A+B$

$-A=B$

So, the motion of the simple harmonic is B.