Differential Equations Question 119
Question: The differential equation of displacement of all “Simple harmonic motions” of given period $ 2\pi /n $ , is
Options:
A) $ \frac{d^{2}x}{dt^{2}}+nx=0 $
B) $ \frac{d^{2}x}{dt^{2}}+n^{2}x=0 $
C) $ \frac{d^{2}x}{dt^{2}}-n^{2}x=0 $
D) $ \frac{d^{2}x}{dt^{2}}+\frac{1}{n^{2}}x=0 $
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Answer:
Correct Answer: B
Solution:
The displacement of x for all S.H.M. is given by $ x=a\cos (nt+b) $
Therefore $ \frac{dx}{dt}=-na\sin (nt+b) $
Therefore $ \frac{d^{2}x}{dt^{2}}=-n^{2}a\cos (nt+b) $
Therefore $ \frac{d^{2}x}{dt^{2}}=-n^{2}x $
Therefore $ \frac{d^{2}x}{dt^{2}}+n^{2}x=0 $ .
BETA
