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 xo and initial velocity Vo. 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 Pl cos (@₁t-a₁). Also, find the undamped position function u(t)= Cocos (@ot-o) 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=25, c=50, k = 169, xo = 5, Vo = 16

Free vibration is a type of vibration in which the external force is removed after giving the initial displacement to a body/system. In other words, in this type of vibration, force is applied at the initial displacement of the system, and after the init…