Problem 2 (30 points) Consider a Single Degree of Freedom System, as depicted below. C m F(t) Part 1 (No Excitation Load) m Initial Position, x Initial Velocity, v stiffness, k Damping Ratio, time step, At 25 MT 0.8 m sec -0.5 m/s 20 KN/m 8% 0.05 sec a) What is the damped natural period of the system? Answer: Ta= b) Perform the first "few" steps of the Taylor method solution to solve for the displacement, x. IF DONE COMPLETELY BY HAND (without the use of Excel or any other computer program), perform three complete steps. IF DONE USING EXCEL, perform 100 steps and graph the results (x vs t). For Part 2, consider an excitation load given by F(t) = 35Sin(0.5t), with F given in KN and t in seconds. c) What is the DAF for this system? Answer: DAF = d) Perform the first "few" steps of the Taylor method solution to solve for the displacement, x. IF DONE COMPLETELY BY HAND (without the use of Excel or any other computer program), perform two complete steps. IF DONE USING EXCEL, perform 100 steps and graph the results (x vs t).