If $x = A \cos 4t + B \sin 4t$, then $\frac{d^2x}{dt^2}$ is equal to:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → $-16x$ ##
$x = A \cos 4t + B \sin 4t$
$\frac{dx}{dt} = -4A \sin 4t + 4B \cos 4t$
$\frac{d^2x}{dt^2} = -16A \cos 4t - 16B \sin 4t$
$= -16(A \cos 4t + B \sin 4t)$
$∴\frac{d^2x}{dt^2} = -16x$