The displacement equation of a particle is $x = 3\sin 2t + 4\cos 2t.$ The amplitude and maximum velocity will be respectively
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(a) $x = 3\sin 2t + 4\cos 2t.$
From given equation ${a_1} = 3,\;{a_2} = 4,$ and $\phi = \frac{\pi }{2}$
$a = \sqrt {a_1^2 + a_2^2} $$ = \sqrt {{3^2} + {4^2}} = 5$
==> ${v_{\max }} = a\omega = 5 \times 2 = 10$
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