Mid Semester Exam-2020 CE 503- Structural Dynamics Submit the answer sheet at amitsh@iitg.ac.in and c.mital@iitg.ac.in In email title write your CE 503-Roll Number. Use Matlab to numerical solve ODE and provide your Matlab script in .m format. Don’t paste your Matlab script in pdf. All Question carries equal marks-20 marks each. .. Question 1. Calculate the solution to . x 2 x 2 x (t ) . x(0) 1; x(0) 0 . Plot the response using Matlab. Question 2. A mass on the pole is modeled by .. .. m x kx y where x and y are as indicated in Figure 1. Assuming the initial conditions are zero, calculate the response of the relative displacement (x – y) if the pole is subject to an earthquake-based excitation of t A 1 y (t ) t0 ;0 t 2t0 0; t 2t0 .. Assume A constant equal to last two digits of your roll number. Question 3. Compute the response of the system in Figure 2 for the case that the damping is linear viscous and the spring is a nonlinear hard spring of the form, k ( x) kx k1 x3 and the system is subject to a harmonic excitation of 300 N at a frequency equal to the natural frequency (ω = ωn) and initial conditions of x0 = 0.01 m and v0 = 0.1 m/s. The system has a mass of 100 kg, a damping coefficient of 170 kg/s and a linear stiffness coefficient of 2000 N/m. The value of k1 is taken to be 10000 N/m3. Compute the solution and compare it to the linear solution (k1 = 0). Provide your Matlab script for evaluation along with the plot. Question 4. Numerically integrate and plot the response of an underdamped system determined by m = 150 kg, and k = 4000 N/m subject to the initial conditions of x0 = 0.01 m and v0 = 0.1 m/s, and the applied force F(t) = F(t) = 15(t 1) , unit step impulse , for various values of the damping coefficient. Use this “Matlab program” to determine a value of smallest damping that causes the transient term to die out with in 3 seconds.