determine the values of the viscous damping coefficient c for which the system has a damping ratio of 0.5 and 1.5

7.47 lb. s/ft

22.42  lb. s/ft

Explanation:

Without mincing words let us dive straight into the solution to the above problem.

STEP ONE: calculate or determine the frequency.

The frequency can be calculated by making use of the formula given below;

frequency, w = √k/m. Thus, frequency = √ 12 × 15/ [40/32.2] = 12 rad/s.

STEP TWO: Determine or calculate for the viscous damping coefficient, c  for damping ratio of 0.5 and 1.5 respectively.

The viscous damping coefficient, c for 0.5 = [ 12 × 0.5 × 2 ×[ 40/32.2] / 2= 7.47 lb. s/ft.

The viscous damping coefficient, c for 1.5= [ 12 × 1.5 × 2 ×[ 40/32.2] / 2 = 22.42  lb. s/ft.

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explanation: