First slide

Simple hormonic motion

Question

The motion of a particle is given by X = A sinωt + B cosωt the motion of the particle is

Easy

A

not simple harmonic
B

simple harmonic with amplitude A+B
C

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

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

Solution

The equation X = (A sinωt + B cosωt)
$\sqrt{A^{2} + B^{2}} \sin (ω t + ϕ) w h e r e ϕ = \tan^{- 1} (\frac{B}{A})$
represents another SHM of time period π/ω having on amplitude
$\sqrt{A^{2} + B^{2}}$
.

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