Question

The displacement equation of a particle is

$x = 3\sin 2t + 4\cos 2t.$ The amplitude and maximum velocity will be respectively

• A. 5, 10
• B. 3, 2
• C. 4, 2
• D. 3, 4

Answer 1

Answer: (A)

5, 10

Answer 2

$x = 3\sin 2t + 4\cos 2t.$ From given equation

$a_{1} = 3,\mspace{6mu} a_{2} = 4,$ and $\varphi = \frac{\pi}{2}$

∴$a = \sqrt{a_{1}^{2} + a_{2}^{2}} = \sqrt{3^{2} + 4^{2}} = 5$⇒$v_{\max}$