Q. 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
Explanation
(a) $x = 3\sin{2t + 4\cos{2t.}}$ From given equation
$a_{1} = 3,a_{2} = 4\ $and $\phi = \frac{\pi}{2}$
$\therefore a = \sqrt{a_{1}^{2} + a_{2}^{2}} = \sqrt{3^{2} + 4^{2}} = 5 \Rightarrow v_{\max} = a\omega = 5 \times 2 = 10$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.