lfa simple pendulum has significant amplitude | vedclass

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Question

The equation of motion for the pendulum, suffering retardation

$I \alpha=-m g(\ell \sin 	heta)-m b v(\ell)$ where $I=m \ell^{2}$

and $\alpha=\m

Vedclass · Accepted Answer

$\frac{2}{b}$

Vedclass · Answer

The equation of motion for the pendulum, suffering retardation

$I \alpha=-m g(\ell \sin 	heta)-m b v(\ell)$ where $I=m \ell^{2}$

and $\alpha=\mathrm{d}^{2} 	heta / d t^{2}$

$	herefore \frac{d^{2} 	heta}{d t^{2}}=-\frac{g}{\ell} 	an 	heta+\frac{b v}{\ell}$

On solving we get $	heta=	heta_{0} e^{-\frac{b t}{2} \sin (\omega t+\phi)}$

According to questions $\frac{	heta_{0}}{e}=	heta_{0} e^{\frac{-b 	au}{2}}$

$	herefore 	au=\frac{2}{b}$

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