The spring has a rest length of r0=1m,g=10m/s2 damping coefficients of br=0.5 and b= 0.2, spring stiffness k=50N/m, and mass m=1kg. The sensed outputs are r(t) and (t). 1. Simulate the Nonlinear System with the following conditions. Use MATLAB's ode45. Create a subplot where the top plot is r vs time, the bottom plot is vs time for 10 seconds. a. Initial Conditions: r=1m,dr/dt=0m/s,=0rad,d/dt=0rad/s, and Inputs ur= 0m/s2,u=0rad/s2 b. Initial Conditions: r=1.2m,dr/dt=0rad/s,=0.5rad,d/dt=0rad/s, and Inputs ur=0m/s2,u=3sin(1.7t)rad/s2 2. Create a simple animation of the pendulum performing the condition in part 1.1c. The animation should depict the changing length of the spring and the bob as a moving circle attached to it. Submit as a .mp4 file. 3. Find the fixed point in the "non-inverted position" or "down position" for the pendulum (=0rad). Verify that it is a fixed point by running a nonlinear simulation with the fixed point as your initial condition, and a plot of r and over time showing that the system does not move (simulate for 5 seconds). 4. Linearize the system about this fixed point and report the matrices for the system in state space form. 5. Simulate the system using MATLAB linear system tools (e.g. 1sim) using the conditions from Part 1.1a and 1.1b and plot the sensed outputs on the same axes as their nonlinear