Aweight is suspended from the ceiling by a spring (k = 20 ln/in) and is connected to the floor by a dashpot producing viscous damping. the damping force is 10 lb when the velocity of the dashpot plunger is 20 in/sec. the weight and plunger have w = 12 lb. what will be the frequency of the damped vibrations?

The frequency of the damped vibrations is 3.82 Hz.

Explanation:

Given that,

Spring constant = 20 lb/in

Damping force = 10 lb

Velocity = 20 in/sec

Weight = 12 lb

We need to calculate the damping constant

Using formula of damping force

Put the value into the formula

We need to calculate the frequency

Using formula of angular frequency

Put the value into the formula

We need to calculate the frequency of the damped vibrations

Using formula of frequency

Put the value into the formula

Hence, The frequency of the damped vibrations is 3.82 Hz.

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