# Mid Semester Exam CE 503 ```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.
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Use Matlab to numerical solve ODE and provide your Matlab script in .m format. Don’t
paste your Matlab script in pdf.
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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.
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