The dynamics of a full-suspension mountain bike can be approximated by the two s

Question

The dynamics of a full-suspension mountain bike can be approximated by the two spring- mass-damper systems shown in the figure. Suppose the total mass (M) of bike and rider is 90 kg, the bike is moving at 30 km/hr. the wheel to wheel distance is 1 m, and the typical bump height is 0.3 m. It is desired that the front suspension displacement Y1 be returned to equilibrium before the rear wheel reaches the point where the front wheel was disturbed. Also, it is desired that the rear wheel return to equilibrium as smoothly as possible. Determine a set of spring and damping constants k1, k2, c1 and c2 that will meet these requirements (note: diagram uses b for the damping constant).

Explanation / Answer

I understand the conern about this Question that's why I am writing this.I saw the same Question while I was used to do Mechanical Engineering Question then also I tried the same problem but was not confident . Hope you are the same asker which put this Question in Mech Engineering and right now also .

my suggestions:

for front tyre:

*keep critical damping for it this will give you a relation between k1 and c1

*find the exact eq in terms of k1 and c1 . keep initial conditions as Y= .3m and Y(dot)=0. now assume some fraction say .99 of .3m then this will give you another relation between k1 and c1 at t= 1m/(30Km/hr)

For rear tyre

consider underdamping eq

keep initial condition at t=0 Y2=0.3m and Y2(dot)=0

now

as smooth as possible so i will suggest you

*keep logarithmic decrement 1

*keep time period of this underdamped motion = 2*1m/(30Km/hr)

Hope you are helped ,you can discuss conveniently .

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