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

The correct option is A $5,10$

$x=3\sin 2t+4\cos 2t$
From the above given equation,
$a_1=3,a_2=4$ and $\varphi =\frac{\pi }{2}$
$\therefore a=\sqrt{a_1^2+a_2^2}=\sqrt{3^2+4^2}=5$
$\Rightarrow v_{\text{max}}=a\omega =5\times 2=10$