Question

# 2. We will plot the responses of many systems in this course, and it is crucial that your plots'titles contain key parameters of the particular system whose response you are showing.The free response of an underdamped SDOF oscillator to initial conditions x(0) = x, and*(0) = v, is x(t)=e^{-\xi \omega_{n} t}\left(x_{0} \cos \left(\omega_{d} t\right)+\frac{v_{0}+\xi \omega_{n} x_{0}}{\omega_{d}} \sin \left(\omega_{d} t\right)\right) \text { where } \omega_{d}=\omega_{n} \sqrt{1-\xi^{2}} \text { is the damped natural frequency of the system. Using the above } equation, plot the response x(t) versus time for a system with natural frequency Wn = 5 rad/sec and damping ratio =0.06 subject to initial conditions x(0)=0 cm and v, = 3 cm/s. Use the linspace command (see Prob. 1 above) to create a time vector with exactly 749 points between t 0 and t 10 sec.automatically, and you may not use a loop to calculate the response. Also, report clearly the value of 700th position in your time vector.The four parameters must be entered Basically, it is expected that you create a time vector and evaluate the equation above for all time with one command. You must turn in both your m-file and your plot.  Fig: 1  Fig: 2  Fig: 3  Fig: 4