If you could include python code on how to generate on single plot that would be very helpful.

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