The remaining problems in this section deal with free damped motion. In Problems 15 through 21, a mass m is attached to both a spring (with given spring constant k) and a dashpot (with given damping constant c). The mass is set in motion with initial position x₀ and initial velocity v₀. Find the position function x(t) and determine whether the motion is overdamped, critically damped, or underdamped. If it is underdamped, write the position function in the form x(t) = C₁e^-pt cos(ω₁t - α₁). Also, find the undamped position function u(t) = C₀ cos(ω₀t - α₀) that would result if the mass on the spring were set in motion with the same initial position and velocity, but with the dashpot disconnected (so c = 0). Finally, construct a figure that illustrates the effect of damping by comparing the graphs of x(t) and u(t).

m = 2 , c = 12, k = 50 ; x₀ = 0, v₀ = -8