Question

A spring with an m-kg mass and a damping constant 8 (kg/s) can be held stretched 1.5 meters beyond its natural length by a force of 7.5 newtons. If the spring is stretched 3 meters beyond its natural length and then released with zero velocity, find the mass that would produce critical damping.

Answer 1

Answer:

3.2 kg

Explanation:

x = Stretched length

k = Spring constant

c = Damping constant

Force

$F=kx\\\Rightarrow k=\frac{F}{x}\\\Rightarrow k=\frac{7.5}{1.5}\\\Rightarrow k=5\ N/m$

For critical damping

$c^2-4mk=0\\\Rightarrow  m=\frac{c^2}{4k}\\\Rightarrow m=\frac{8^2}{4\times 5}\\\Rightarrow m=3.2\ kg$

The mass that would produce critical damping is 3.2 kg