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Question Number 34988 by ajfour last updated on 14/May/18

Commented by ajfour last updated on 14/May/18

$$Ifatunnelisdugacrossa$$$$diameterofEarthandarod$$$$ofmassmfreetooscillate$$$$aboutthistunnelisdisplaced$$$$slightlyandreleased,findthe$$$$timeperiodofsmalloscillations.$$

Answered by ajfour last updated on 14/May/18

$$F\left(x\right)=-\frac{2GM\lambda x}{R^2};(\mathrm{\forall }\lambda =\frac{m}{2R})$$$$\frac{d^{2}x}{{dt}^2}=-\left(\frac{GM}{R^3}\right)x\Rightarrow {\omega }^2=\sqrt{\frac{GM}{R^3}}$$$$T=\frac{2\pi }{\omega }=2\pi \sqrt{\frac{R^3}{GM}}.$$

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