Home /
Expert Answers /
Mechanical Engineering /
solve-number-3-figure-1-cart-with-simple-pendulum-this-mechanisin-has-one-translational-degrce-of-pa285

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 $C$ with mass $m_{1}$ and center of mass $c$ rolls along ia as shown in Figure 1. The distance from $w$ to $c$ along $iA$ is $q.A$ simple pendulum $L$ with length $f$ is connected to the cart at $c_{1}$, and the particle $y$ mountod on the end of the pendulum has mass m2. As shown in the Figure, an external force $f _{ext}=f_{ext}l^_{A}$ is applied to the cart. The cquation of motion of the cart and the pendulum is $[m_{1}+m_{2}m_{2}ℓcosθ m_{2}ℓcosθm_{2}ℓ_{2} ][qθ ]+[−m_{2}ℓθ˙_{2}sinθm_{2}ℓgsinθ ]=[f_{cxt}0 ].$
\begin{tabular}{|c|c|} \hline Parameter & Value \\ \hline Mass of the cart, $m_{1}$ & $2kg$ \\ \hline Mass of the pendulum, $m_{2}$ & $1.kg$ \\ \hline Length of the pendulum, $ℓ$ & $30cm$ \\ \hline Acceleration due to gravity, $g$ & $10m/s_{2}$ \\ \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.

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:

Live Sessions

Online Lab Report Help

Online Project Report Help

Online Assignment Help

Essay Writing Help

CPM Homework Help

Mortgage Calculator

Electrical Engineering

Civil Engineering

Chemical Engineering

Electronics and Communication Engineering

Mathematics

Physics

Chemistry

Software Works/ Computer Science

Other Subjects

100% Correct Solutions

24/7 Availability

One stop destination for all subject

Cost Effective

Solved on Time

Plagiarism Free Solutions

Confidentiality