The potential energy of a particle of mass $100 \,g$ moving along $x$-axis is given by $U=5 x(x-4)$, where $x$ is in metre. The period of oscillation is .................
Diffcult
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(a)
Given, mass of particle $=100 g =0.1 kg$ potential energy, $U=5 x(x-4)$
$U=5 x^2-20 x$
Now, let force be $F$ :
$F=-\frac{d U}{d x}=-(10 x-20)$
Also, $\quad F=-k x$
So, $\quad f=-10(x-2)$.
To simplify, $\quad f=-10 x$
So, $-10 x $$=-k x $$ k $$=10 $
$k=10$
So, time period, $T=2 \pi \sqrt{\frac{m}{r}}$
$T=2 \pi \sqrt{\frac{0.1}{10}}$
$T=0.2 \pi sec$
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