PHI 203 Midterm: PHYS 203 Princeton MidFall2005
Document Summary
A small ball of mass m is released with a zero velocity from a height h above the floor. Now suppose there absence of air resistance the ball will hit the floor in a time is a small resistance force proportional to the velocity, f= kmv. For small k the time increment t1 is the floor will increase by a small amount gh. 1 proportional to k: determine the equation describing the position of the ball as a function of time, calculate t1 to first non-trivial order in k. For your reference the taylor series is given by xf x xf. 0 n x n: the equation of motion is (x axis is directed down) xm. The characteristic equation for the homogeneous differential equation solution can be guessed tkg x. Hence the complete solution to the equation of motion is kr. )0( constants a and b have to satisfy the following two equations.
