Question

The displacement equation of a simple harmonic oscillator is given by
$A\sin \omega t-B\cos \omega t$
The amplitude of the oscillator will be :

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

Answer 1

The correct option is C $\sqrt{A^2+B^2}$

Displacement equation
$y=A\sin \omega t-B\cos \omega t$
Let $A=a\cos \theta$ and $N=a\sin \theta$
So, $A^2+B^2=a^2$
$\Rightarrow$ $a=\sqrt{A^2+B^2}$
Then $y=a\cos \theta \sin \omega t-a\sin \theta \cos \omega t$
$y=a\sin (\omega t-\theta )$
which is the equation of simple harmonic oscillator
The amplitude of the oscillator
$a=\sqrt{A^2+B^2}$