Suppose that a hole is now drilled directly from the surface of the Earth at the North Pole, all the way through the centre to the surface at the South Pole. A particle of mass m is dropped into this hole from a resting position at the North Pole at time $t = 0$ Suppose that the particle is subjected to a viscous resistive drag force proportional to the mass of the particle and its velocity:
:$ F_D$ = β[$\frac{ d r(t)}{dt}]^2$ sgn$\frac{dr(t)}{dt}$, where sgn(x) = $\frac{x}{ |x|}$ is the sign of variable x. ,$ k^2 = GM/R^3 = g/R$ and the equation becomes $\frac{d^2r}{dt^2}$=-β[$\frac{ d r(t)}{dt}]^2$ sgn$\frac{dr(t)}{dt}$-$k^2$r(t)
a)In this case, the equation of motion cannot be solved analytically using the methods that we have developed in class. Using the Maple procedure RungeKuttaIVP 2D, find the numerical solution to equation (3) for $\beta = 10−7$ and (ii) $\beta = 10−2$ and, by plotting solutions on a single graph over the same timespan as in Q2(b), show that the motion exhibits damped oscillations in one of these cases but not the other.
Ok, so from this question I have set the initial conditions using the above information, $ICS = r(0)=R$, $(D(r))(0)=0$;
and I tried solving it with maple
really stuck from there any help will be appreciated.