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Mass Spring damper system

1. The problem statement, all variables and given/known data

If an aeroplane of a mass of = 5000 with a velocity of ̇ = 500/ℎ has to land on a daily
basis what would be your design characteristic of a damping system to absorb the ground energy
contact within 5 seconds.
Hint: Your answers may include:

i. The values of k (the spring stiffness), C (the damping coefficient), Cc (the critical damping) etc.

ii. Matlab code, graphs and comments to illustrate your solution.


2. Relevant equations


3. The attempt at a solution

as spring stiffness and damping ratio is not given in the question and I was told to keep changing the spring stiffness and damping ratio in MATLAB until you get a smooth curve, an oscillation which dies after 5 seconds. that is why i started with MATLAB, graph and coding is attached below.
i am using unforced method, not sure if it is right or not, my only concern is damping ratio. which is 4.5 in this case. normally if damping ratio < 1 ... it is under damped. if equal to 1 than critical damped. bigger then 1 over damped..
in my case it is bigger that 1 so must be over damped but graph looks like critical damped.

i tried this question with forced method as well. but i dont know how to calculate the force required aircraft function.JPG aircraft graph.JPG few friends said F=kx, but i dont know how to calculate x in order to find F,
 
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