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Question Number 23492 by ajfour last updated on 31/Oct/17

Commented by ajfour last updated on 31/Oct/17

$$Findtheperiodofsmall$$$$oscillationsofthedisc,if$$$$springsareattachedata$$$$distanceof\mathit{a}fromthe$$$$frictionlesshinge.$$

Commented by mrW1 last updated on 31/Oct/17

$$\mathrm{I}=\frac{{\mathrm{MR}}^2}{2}$$$$\tau =-{2\mathrm{a}}^2\mathrm{k}\vartheta$$$$\mathrm{T}=2\pi \sqrt{\frac{{\mathrm{MR}}^2}{2\times {2\mathrm{a}}^2\mathrm{k}}}=\frac{\pi \mathrm{R}}{\mathrm{a}}\sqrt{\frac{\mathrm{M}}{\mathrm{k}}}$$

Commented by ajfour last updated on 31/Oct/17

$$yessir,thanksforsolving..$$

Commented by ajfour last updated on 31/Oct/17

$$Mgevencontributesapositive$$$$torque..{shouldn}^{\prime }tthatbeeven$$$$takenintoaccount?$$

Commented by mrW1 last updated on 31/Oct/17

$$\mathrm{then}$$$$\tau =-{2\mathrm{a}}^2\mathrm{k}\vartheta +\mathrm{Mgc}\theta =-({2\mathrm{a}}^2\mathrm{k}-\mathrm{Mgc})\theta$$$$\mathrm{c}=\frac{4\mathrm{R}}{3\pi }$$$$\mathrm{T}=2\pi \sqrt{\frac{{\mathrm{MR}}^2}{2\times ({2\mathrm{a}}^2\mathrm{k}-\mathrm{Mgc})}}=\frac{\pi \mathrm{R}}{\mathrm{a}}\sqrt{\frac{\mathrm{M}}{\mathrm{k}-\frac{2\mathrm{MgR}}{3\pi {\mathrm{a}}^2}}}$$

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