The differential equation of the simple harmonic motion given by $x = A cos (n t + α)$ is

\frac{d^{2} x}{d t^{2}} - n^{2} x = 0

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\frac{d^{2} x}{d t^{2}} + n^{2} x = 0

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\frac{d x}{d t} - \frac{d^{2} x}{d t^{2}} = 0

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\frac{d^{2} x}{d t^{2}} - \frac{d x}{d t} + n x = 0

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Solution

The correct option is B $\frac{d^{2} x}{d t^{2}} + n^{2} x = 0$
Given, $x = A cos (n t + α)$
Thus $\frac{d x}{d t} = - A sin (n t + α) n$
$\Rightarrow \frac{d^{2} x}{d t^{2}} = - A cos (n t + α) n^{2} = - n^{2} x$
Therefore, $\frac{d^{2} x}{d t^{2}} + n^{2} x = 0$

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The differential equation of the simple harmonic motion given by x=Acos(nt+α) is

The correct option is B d2xdt2+n2x=0Given, x=Acos(nt+α)Thus dxdt=−Asin(nt+α)n⇒d2xdt2=−Acos(nt+α)n2=−n2xTherefore, d2xdt2+n2x=0

The differential equation of the simple harmonic motion given by $x = A cos (n t + α)$ is

The correct option is B $\frac{d^{2} x}{d t^{2}} + n^{2} x = 0$
Given, $x = A cos (n t + α)$
Thus $\frac{d x}{d t} = - A sin (n t + α) n$
$\Rightarrow \frac{d^{2} x}{d t^{2}} = - A cos (n t + α) n^{2} = - n^{2} x$
Therefore, $\frac{d^{2} x}{d t^{2}} + n^{2} x = 0$