FIGURE P23.15 Problem 23.15. Consider an Inverted Pendulum of length L 0.5 m as shown in Figure P23.15 (Chapra 3rd edition). This system can be modeled using the following differential equations dt dt L where ?(t) is the angle of the Inverted Pendulum with respect to the y-axis, and w(t) is the angular velocity. Given the initial values of ?(0) = 0 and w(0) = 0.25 rad/s (a) Using Euler m ethod. plot ?(t) and w(t) versus time from t = 0 to 2 seconds in MATLAB (b) The angle ? of the Inverted Pendulum can not exceed ?/2 and the angular velocity w should become zero once ? reaches ?/2. Modify your code to include such constrains