Question

For a dynamical system, the equations of motion in motesi coordinates are given as

y₁ + 0.02 y₁ + 4y₁ = 0
y₂ +0.3y₂ +5y₂ = 0
1. Determine the natural frequencies.
2. Determine the damping rations.

Answer 1

The natural frequencies for the dynamical system are both 0.

Step-by-step explanation:

To determine the natural frequencies of the dynamical system, we need to solve the equations of motion for y₁ and y₂. For the first equation, we have y₁ + 0.02y₁ + 4y₁ = 0, which simplifies to (1 + 0.02 + 4)y₁ = 0. So, the natural frequency for y₁ is 0.

For the second equation, we have y₂ + 0.3y₂ + 5y₂ = 0, which simplifies to (1 + 0.3 + 5)y₂ = 0. So, the natural frequency for y₂ is 0 as well.