Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# The Motion of a Particle is Given by X = a Sin ωT + B Cos ωT. the Motion of the Particle - Physics

MCQ

The motion of a particle is given by x = A sin ωt + B cos ωt. The motion of the particle is

#### Options

• not simple harmonic

• simple harmonic with amplitude A + B

• simple harmonic with amplitude (A + B)/2

• simple harmonic with amplitude

#### Solution

simple harmonic with amplitude $\sqrt{A^2 + B^2}$

x = A sin ωt + B cos ωt      ...(1)

$\text { Acceleration },$

$a = \frac{\text {d}^2 x}{\text {dt}^2} = \frac{\text {d}^2}{\text{dt}^2}(\text {A}\sin\omega t + \text {B} \cos \omega t)$

$= \frac{\text{d}}{\text {dt}}(\text { A }\omega \cos \omega t - \text { B }\omega \sin \omega t)$

$= - \text { A } \omega^2 \text { sin }\omega t - \text { B }\omega^2 \cos \omega t$

$= - \omega^2 (\text { A }\sin \omega t + \text { B }\cos \omega t )$

$= - \omega^2 x$

For a body to undergo simple harmonic motion,
acceleration, a =$-$ kx.     ...(2)

Therefore, from the equations (1) and (2), it can be seen that the given body undergoes simple harmonic motion with amplitude,  A

$= \sqrt{A^2 + B^2}$

Is there an error in this question or solution?

#### APPEARS IN

HC Verma Class 11, 12 Concepts of Physics 1
Chapter 12 Simple Harmonics Motion
MCQ | Q 7 | Page 250