Differentiation Question 396
Question: If $ x=A\cos 4t+B\sin 4t $ ,then $ \frac{d^{2}x}{dt^{2}}= $
[Karnataka CET 2004]
Options:
A) - 16x
B) 16 x
C) x
D) - x
Show Answer
Answer:
Correct Answer: A
Solution:
$ x=A\cos 4t+B\sin 4t $
Differentiate w.r.t. t, $ \frac{dx}{dt}=-4A\sin 4t+4B\cos 4t $
Again, differentiate w.r.t. t, $ \frac{d^{2}x}{dt^{2}}=-16A\cos 4t-16B\sin 4t $
$ \frac{d^{2}x}{dt^{2}}=-16[A\cos 4t+B\sin 4t] $ . Hence, $ \frac{d^{2}x}{dt^{2}}=-16x $ .
BETA
