Question

For the system given below, find time period of oscillation?

• A. $\frac{10}{\sqrt{3}}$
• B. $10\sqrt{3}$
• C. $\frac{20}{\sqrt{3}}$
• D. $20\sqrt{3}$

Answer 1

Answer: (C)

$\frac{20}{\sqrt{3}}$

Answer 2

By energy method $\frac{1}{2}Kx^{2}+\frac{1}{2}mv^{2}+\frac{1}{2}l\omega^{2}=C$ $\frac{1}{2}.K.2x.\frac{dx}{dt}+\frac{1}{2}.m.2v \frac{dv}{dt}+\frac{1}{2}I.+\frac{2v}{r^{2}} \frac{dv}{dt}=0$ $Kxv +\frac{M}{4}va+\frac{M}{2}a.v=0$ $-Kx=\frac{3Ma}{4}$ $a=-\frac{4K}{3M}.x=-\omega^{2}x$ $\omega^{2}=\frac{4K}{3M}$ $\omega=\sqrt{\frac{4K}{3M}}=\sqrt{\frac{4\times100}{3\times1}}=\frac{20}{\sqrt{3}}$ sec