If $x = A\cos{4t} + B\sin{4t}$, then $\frac{d^{2}x}{dt^{2}}$ is equal to

Question

Dr. Abubacker · Accepted Answer

(a)
Given, $x = A\cos{4t} + B\sin{4t}$ …(i)
$\Rightarrow$ $\frac{dx}{dt} = - 4A\sin{4t} + 4B\cos{4t}$
$\Rightarrow$ $\frac{d^{2}x}{dt^{2}} - 16A\cos{4t} - 16\ B\sin{4t}$
$\Rightarrow$ $\frac{d^{2}x}{dt^{2}} = - 16x$ [from Eq. (i)]

Q. If $x = A\cos{4t} + B\sin{4t}$, then $\frac{d^{2}x}{dt^{2}}$ is equal to

Explanation

Reviewed by Dr. Abubacker

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