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  • Q1: f. Using Matlab, plot the unit step response of your closed loop system with these gains to a stepchange in reference input. Use zero initial conditions. (Submit a printout of your Matlab code andyour plot.) What happened? Did you get the response you want?See Answer
  • Q2:The behavior of an isotropic non-linear material is described by Green elastic expression and where a, b, c are constants. Please ( a ) derive the stress-strain relations for this material; ( b ) show that the constitutive equations are reduced to those of the isotropic linear elastic material for c = 0; ( c ) find the elastic moduli E and for this case. See Answer
  • Q3: Example 2.7 in the 7th edition of the FPE textbook describes a model for an inverted cart-and-pendulum system that is similar to the Segway scooter. Let's take a more detailed look at what is neededto balance an inverted pendulum or Segway. a. First, start with the equations of motion for this system that are given in the book (equation 2.30): \begin{array}{l} \left(I+m_{p} l^{2}\right) \ddot{\theta}^{\prime}-m_{p} g l \theta^{\prime}=m_{p} l \ddot{x} \\ \left(m_{t}+m_{p}\right) \ddot{x}+b \dot{x}-m_{p} l \ddot{\theta}^{\prime}=u \end{array} Derive the transfer function from the cart input U(s)to the angle O'(s).See Answer
  • Q4:The stress tensor at a point under the working condition is given by See Answer

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