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Answer:
the damping coefficient when the system is critically damped is 13.42 lb s/ft.
Explanation:
The directions are missing the last part, which is:
"A mass weighing 30 lb stretches a spring 7.5 in. The mass is also attached to a damper with coefficient γ. Determine the value of γ for which the system is critically damped. Assume that
Round your answer to three decimal places."
The spring system is determined by the following differential equation
where is the damping coefficient, thus it is critically damped when the system transitions from real to complex solutions that happens at
Solving for the damping coefficient.
where the spring constant k is given by
And the mass is given by
So the damping coefficient will be
Replacing the given information we have:
Thus we get
The value of the damping coefficient when the system is critically damped is 13.42 lb s/ft.