Does the Mass Affect the Damping Coefficient in Spring Oscillations?

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Just a quick question that I am unsure about. Let say a vertically suspended spring with an attached mass at the bottom. How does the mass relate to the damping coefficient?

I am guessing that the mass is proportional to the damping coefficient. The heavy the mass at the end, the higher the damping coefficient which causes the spring oscillation to die faster than a lighter mass.

Am i right? If not please correct me and explain. thanks a lot.
 
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The spring with the larger mass will oscillate slower, the damping depends on velocity, so there will be less energy lost in each cycle for a larger mass.
 
The mass is released at rest at height A, does this give more information about the damping?