First slide

Simple harmonic motion

Question

The displacement equation of a particle is $x = 3 \sin 2 t + 4 \cos 2 t .$ The amplitude and maximum velocity will be respectively

Moderate

A

5, 10
B

3, 2
C

4, 2
D

3, 4

Solution

$x = 3 \sin 2 t + 4 \cos 2 t .$ From given equation
$a_{1} = 3, a_{2} = 4,$ and $φ = \frac{π}{2}$
$∴ a = \sqrt{a_{1}^{2} + a_{2}^{2}}$ $= \sqrt{3^{2} + 4^{2}} = 5$
$\Rightarrow v_{\max} = aω = 5 \times 2 = 10$

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