assumptions:(adsbygoogle = window.adsbygoogle || []).push({});

Earth is spherical, and it's density uniform.

Me, G, r(earth) are known, m(object) is not known

How fast is the object travelling when it passes the centre, and what is the period of it's oscillation ??

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x(t) = r cos wt

(r is the magnitude of the harmonic motion, radius of earth)

x(t) at centre = 0, thus (wt) = pi/2

v(t) = -r w sin(wt) by differentiation x(t)

sin(wt) = 1,

v = -rw

w = sqrt(k/m), m is the object dropped

k = GMmr^-2, ie the Grav. force

so we can get wr = sqrt(G * Me)

about 19962000 m/s

Does this look OK so far ?

working out T (similar to above, T = 2 pi/w ) i got about 2s, WTF that can't be right.

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# Mass dropped into hole through Earth

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