Write the correct alternative in the following:

Question:

Write the correct alternative in the following:

If $x=a \cos n t-b \sin n t$, then $\frac{d^{2} x}{d t^{2}}$ is

A. $n^{2} x$

B. $-n^{2} x$

C. $-n x$

D. $n x$

Solution:

Given:

$x=a \cos n t-b \sin n t$

$\frac{\mathrm{dx}}{\mathrm{dt}}=-\mathrm{an} \sin \mathrm{nt}-\mathrm{bn} \cos \mathrm{nt}$

$\frac{d^{2} x}{d t^{2}}=-a n^{2} \cos n t+b n^{2} \sin n t$

$=-n^{2}(a \cos n t-b \sin n t)$

$=-n^{2} x$

 

Leave a comment

None
Free Study Material