Problem 5: Consider a mass-spring-damper system (underdamped) with an excitation F(t) = Fous(t) applied on the particle, where Fo is a constant, and us(t) is the unit step function. The mass of the particle m, the stiffness of the spring k, and the damping coefficient of the dashpot c are given. The equation of motion is as follows: x k Underdamped Fit) Fit) = Fo us it) + + = Fo us(t) EOM m The step response with initial conditions x(0) = 0, x (0) = 0 is plotted as follows: x(t)n (1+ Be-sunt) J= Mp dst (1-Be-sunt) t tr tp xit)= dst (1-e -sunt (cos(wat)+ Wd where dst= , Wd = Wn 1-52 Sin (Wa (wat))) where dst = Fo k = is called the static deformation. Calculate the rise time t, when x(t) first reaches the static deformation, and the overshoot Mp when x(t) reaches the maximum value (note: x(t) = O at the maximum point).