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# question.pdf - Eng6933 Problem Sets 1 Problem Set 1 1 Write...

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Eng6933 - Problem Sets 1 1 Problem Set 1 1. Write a MatLab program to plot Eqs. (17), (20) and (21) in the notes versus time. The inputs should be system mass, m , linear spring con- stant, k , and the initial system displacement, x o , and velocity, ˙ x o . Play with the program in- putting various values of m , k , and initial condi- tions. Observe the behaviour of the various am- plitudes, natural frequencies and phase angles. 2. Write a MatLab program to plot Eq. (38) in the notes versus time. The inputs should be sys- tem mass, m , linear spring constant, k , damping ratio ( ζ < 1), and the initial system displace- ment, x o , and velocity, ˙ x o . Play with the pro- gram inputting various values of m , k , ζ and initial conditions. Observe the behaviour of the various amplitudes, damped frequency of oscil- lation, phase angles, and number of oscillations before the system returns to the equilibrium con- dition. 3. Differentiate Eq. (38) to obtain the system accel- eration. Include this expression in the program for 2 above. What happens to the acceleration as ζ 1? Do you want to ride in a car with high damping? Why? 4. Write a MatLab program to plot Eq. (48) in the notes. The inputs should be system mass, m , linear spring constant, k , damping ratio ( ζ > 1), and the initial system displacement, x o , and velocity, ˙ x o . Play with the program inputting various values of m , k , ζ and initial conditions. Observe the behaviour of the various amplitudes, and time required for the system to return to equilibrium. Note: Do this in groups if you wish (perhaps your lab group), it is for education purposes. In previous years, students commented that doing this sort of stuff really helped with understand- ing the course material. You can do the plots with other software (e.g. Excel) but practice in MatLab will help later in the course, especially the labs. I will not provide solutions for this

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