A particle in SHM has displacement $x = a\cos(\omega t) + b\sin(\omega…

Question

A particle in SHM has displacement $x = a\cos(\omega t) + b\sin(\omega t)$. The amplitude of motion is:

Accepted Answer

B. $\sqrt{a^2 + b^2}$

**Express as single sinusoid:** $x = R\sin(\omega t + \phi)$ with $R\sin\phi = a$ and $R\cos\phi = b$.
So $R^2 = a^2 + b^2$ ⇒ $R = \sqrt{a^2+b^2}$.
(Classic Asin + Bcos identity.)

Answer

$|a| + |b|$

Answer

$\sqrt{a^2 - b^2}$

Answer

$\max(|a|,|b|)$

A particle in SHM has displacement $x = a\cos(\omega t) + b\sin(\omega t)$. The amplitude of motion is:

Keep practising Unit 1A: Kinematics: 1D Motion, Position & Velocity