- #1
astenroo
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Homework Statement
View the Earth as a homogenous sphere with the density [tex]\rho[/tex]. Assume a hole has been succesfully been drilled through the center of the Earth, and a body with mass m is dropped down the hole. Give an expression of the force as function of of the distance r from the Earth's centre. Show that this force gives rise to a harmonic oscillation, and give the period for the motion. Assume m = 1 kg. What is the velocity and kinetic energy at passing the centre?
I've seen this has been tried earlier, but I would like to give a shot at it myself. I'm currently taking a course in maths (methods for physicists) and the current topic is differential equations.
Ok, here goes
Homework Equations
F=-kx (this is what I need to show)
The Attempt at a Solution
So, this is where I think I should start out.
F=Gm [tex]\frac{dM}{dr^{2}}[/tex]
or
m[tex]\frac{d^{2}r}{dr^{2}}[/tex]=Gm[tex]\frac{dM}{dr^{2}}[/tex]
So, am I on the right track or am making this more complicated than it is? Hints would be very nice at this stage. I have a hunch I'll end up with complex numbers...