Please show the python code you use, will be sure to rate, thanks!

1. For a mass-damper-spring system of which the EOM is given as m + c + kY = mg, draw the vibration responses in a single plot with the initial displacement of Yo 0.001 m and the initial velocity of Yo 1 m/s for three undamped vibration cycles, when the undamped natural frequency is 100 Hz and the damping ratios are 0.1, 1, 1.8, and 3. The gravitational acceleration g is given as 9.81 m/s2. Discuss the vibration characteristics in terms of the damping ratios. In your solution procedure, clearly show how to obtain the two constants in the homogeneous solution. Submit your Matlab or Python code to generate the single plot. 1. For a mass-damper-spring system of which the EOM is given as m + c + kY = mg, draw the vibration responses in a single plot with the initial displacement of Yo 0.001 m and the initial velocity of Yo 1 m/s for three undamped vibration cycles, when the undamped natural frequency is 100 Hz and the damping ratios are 0.1, 1, 1.8, and 3. The gravitational acceleration g is given as 9.81 m/s2. Discuss the vibration characteristics in terms of the damping ratios. In your solution procedure, clearly show how to obtain the two constants in the homogeneous solution. Submit your Matlab or Python code to generate the single plot