Question

A mass weighing 7 lb stretches a spring 1.5 in. The mass is also attached to a damper with coefficient γ. Determine the value of γ for which the system is critically damped. (Use g = 32ft/s2 for the acceleration due to gravity

Answer 1

Answer:

γ =7 slug/s

Explanation:

See attachment below.

Answer 2

The value of γ will be "7 slug/s".

Mass and Acceleration

According to the question,

Mass with weight, W = 7 lb

Length of spring, x = 1.5 in or,

                                = $\frac{1.5}{12}$

                                = 0.125 ft

Acceleration due to gravity, g = 32 ft/s²

As we know,

→ K = $\frac{W}{x}$

By substituting the values,

     = $\frac{7}{0.125}$

     = 56 lb/ft

As we know,

m = $\frac{W}{g}$

   = $\frac{7}{32.17}$

hence, The value will be:

→ γ = 2√km  

By substituting the values, we get

     = 2√56×$\frac{7}{32}$

     = 7 slug/s

Thus the response above is appropriate.

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