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Property 5

If x=A cos 4t...

Question

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

A

$- 16 x$

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B

$16 x$

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C

$x$

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D

$- x$

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Solution

The correct option is A
$- 16 x$

Explanation for the correct option.
$\begin{array}{rcl} x & = & A \cos 4 t + B \sin 4 t \\ \Rightarrow \frac{d x}{d t} & = & - 4 A \sin 4 t + 4 B \cos 4 t \\ \Rightarrow & \frac{d^{2} x}{d t^{2}} = - 16 A \cos 4 t - 16 B \sin 4 t \\ = & - 16 (A \cos 4 t + B \sin 4 t) \\ = & - 16 x \end{array}$
Hence, option A is correct.

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