I Consider a damped nndriven oscillator whose equation of motion is given by _ . '3 . a, ags, 1;, Assume that the system is critically damped. such that 1; = 2%. 1il'ir'hen this is the case. a general solution is given by If!) : [A + SHETUE I where A and B are constants. A) Express the general solution as a complex function. [Hint This is a trick question] B) Assume the oscillator is initially at rest at the origin. Att = I], it is given an impulse T {i.e.. a sudden blow), causing it to launch with initial positive velocity.r vo. Determine specific expression for both kit} and vitj in terms of known values. C} Determine both the time when the velocity is zero and The time when the velocity.r starts to increase {i.e.. when the acceleration changes sign}. D} Extending from parts h and c. sketch both x} and vtt). making sure to clearly indicate The relevant values {e.g., the maximum displacement. etc...}. [Hint: The velocity.r is zero when the object is at the maximum displacement