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(Solved): solve number 3 Figure 1: Cart with simple pendulum. This mechanisin has one translational degrce of ...

solve number 3

Figure 1: Cart with simple pendulum. This mechanisin has one translational degrce of frecdom arid one rotational degree of freedom. The system physically consists of a cart with mass and center of mass rolls along ia as shown in Figure 1. The distance from to along is simple pendulum with length is connected to the cart at , and the particle mountod on the end of the pendulum has mass m2. As shown in the Figure, an external force is applied to the cart. The cquation of motion of the cart and the pendulum is \begin{tabular}{|c|c|} \hline Parameter & Value \\ \hline Mass of the cart, & \\ \hline Mass of the pendulum, & \\ \hline Length of the pendulum, & \\ \hline Acceleration due to gravity, & \\ \hline \end{tabular} 3. Lineariazation. Lincarize the nonlincar system (1) about all cquilibriums you found in the previous step. At each equilibrium, classify the linearized system as asymptotically stable, semi-stable, Lyapunov stable, or unstable.

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To linearize the given nonlinear system and analyze its stability, we'll use the Jacobian matrix. Here's the Matlab code that performs the linearization and stability analysis for each equilibrium point:
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