Oh my god. This is incredibly simple. I over complicated it I guess. So I have
C=\dfrac{3\pi a^2}{2}
2\pi ax- \dfrac{\pi x^2}{2}=-kx+\dfrac{3 \pi a^2}{2}
x=0 when t=T
kT=\dfrac{3 \pi a^2}{2}
k=\dfrac{3 \pi a^2}{2T}
Got it.
My physics sucks but does gravity affect electical charges inside devices... Does it affect magnetism in coils... I thought it has an affect on anything regardless of how small it is.. right?
A hemispherical bowl of radius a has its axis vertical and is full of water. At time t=0 water starts running out of a small hole in the bottom of the bowl so that the depth of water in the bowl at t is x. The rate at which the volume of water is decreasing is proportional to x. Given that the...