Question-34988

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

Commented by ajfour last updated on 14/May/18

I f a t u n n e l i s d u g a c r o s s a

d i a m e t e r o f E a r t h a n d a r o d

o f m a s s m f r e e t o o s c i l l a t e

a b o u t t h i s t u n n e l i s d i s p l a c e d

s l i g h t l y a n d r e l e a s e d, f i n d t h e

t i m e p e r i o d o f s m a l l o s c i l l a t i o n s .

Answered by ajfour last updated on 14/May/18

F (x) = - \frac{2 G M λ x}{R^{2}}; (\forall λ = \frac{m}{2 R})

\frac{d^{2} x}{{d t}^{2}} = - (\frac{G M}{R^{3}}) x \Rightarrow ω^{2} = \sqrt{\frac{G M}{R^{3}}}

T = \frac{2 π}{ω} = 2 π \sqrt{\frac{R^{3}}{G M}} .

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