The Oscillating Pendulum A particle with a mass m = 100 gr is suspended vertically from a spring with a spring constant of k' = 40 N/m (note that for a linear spring the force is proportional to Icy, where y is the position). The particle is pulled 2 cm below its equilibrium position, and given an upward velocity of 10 mfs. The governing equation for the particle's position at time t is given by where m is in kg, y in meters, and t is in seconds. (a) The governng equation is a secondorder ODE. Specify the two initial conditions that we need in order to determine the complete solution. (b) Solve the governing equation and use the initial conditions to determine its two constants. (c) Determine the amplitude, period, and frequency of the oscillations. To do so, write the solution in (b) as Asinut | 6'), and determine A, w, and H. (d) Determine the times at which the particle has a velocity of zero