The equations of motion for the pendulum, considering gravitational and damping forces, and a step input...

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The equations of motion for the pendulum, considering gravitational and damping forces, and a step input applied at t = 0 are derived as follows: ml+b0+ mgl sin(0) = Fstep (t) where Fstep (t) represents the step force applied at t = : 0, modeled as a Heaviside step function. The damping coefficient b is a measure of the resistive forces acting against the motion of the pendulum. The gravitational force has a component mgl sin(0) due to the pendulum's displacement angle 0. You may consider m, l, and g as given, with m = 1 kg, l = 1 m, and g = 9.81 m/s. Assignment Tasks Simulation Create a Simulink model to simulate the pendulum's motion over 10 seconds. Vary the damping coefficient b to observe different behaviors (underdamped, critically damped, overdamped) and measure the following response characteristics to the step input: 1. Rise Time 2. Peak Time 3. Overshoot 4. Settling Time 5. Steady-State Error The equations of motion for the pendulum, considering gravitational and damping forces, and a step input applied at t = 0 are derived as follows: ml+b0+ mgl sin(0) = Fstep (t) where Fstep (t) represents the step force applied at t = : 0, modeled as a Heaviside step function. The damping coefficient b is a measure of the resistive forces acting against the motion of the pendulum. The gravitational force has a component mgl sin(0) due to the pendulum's displacement angle 0. You may consider m, l, and g as given, with m = 1 kg, l = 1 m, and g = 9.81 m/s. Assignment Tasks Simulation Create a Simulink model to simulate the pendulum's motion over 10 seconds. Vary the damping coefficient b to observe different behaviors (underdamped, critically damped, overdamped) and measure the following response characteristics to the step input: 1. Rise Time 2. Peak Time 3. Overshoot 4. Settling Time 5. Steady-State Error