A spring with an 772kg mass and a damping constant 5 kgs can

A spring with an 772-kg mass and a damping constant 5 (kg/s) can be held stretched 1 meters beyond its natural length by a force of 2 newtons. If the spring is stretched 2 meters beyond its natural length and then released with zero velocity, find the mass that would produce critical damping.

Solution

Force = spring constant * distance

Spring constant k = force / distance = 2 Newton per metre

Critically damping constant = 2 sqrt (k*m)

5 = 2 sqrt ( 2m)   

2m = 25/4

m = 25/8 kg

 A spring with an 772-kg mass and a damping constant 5 (kg/s) can be held stretched 1 meters beyond its natural length by a force of 2 newtons. If the spring is

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