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A 64 lb weight is attached to the lower end of a coil spring suspended from the ceiling, the spring constant being 18 lb/ft. The weight comes to rest in its equilibrium position. It in then pulled down 6 inches below its equilibrium position and released at t = 0. At this instant, an external force given by F(t) = 3 cos wt is applied to the system. (i) Assuming the damping force in pounds is numerically equal to 4(dx/dt), where dx/dt is the instantaneouse velocity in feet per second, find the displacement as a function of the time and determine the resonance frequency of resulting motion. (ii) (ii) Assuming there is no damping, determine the value of w which gives rise to undamped resonance.

A 64 lb weight is attached to the lower end of a coil spring suspended from the ceiling, the spring constant being 18 lb/ft. The weight comes to rest in its equilibrium position. It in then pulled down 6 inches below its equilibrium position and released at t = 0. At this instant, an external force given by F(t) = 3 cos wt is applied to the system. (i) Assuming the damping force in pounds is numerically equal to 4(dx/dt), where dx/dt is the instantaneouse velocity in feet per second, find the displacement as a function of the time and determine the resonance frequency of resulting motion. (ii) (ii) Assuming there is no damping, determine the value of w which gives rise to undamped resonance.

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A 64 lb weight is attached to the lower end of a coil spring suspended from the ceiling, the spring constant being 18 lb/ft. The weight comes to rest in its equilibrium position. It in then pulled down 6 inches below its equilibrium position and released at t = 0. At this instant, an external force given by F(t) = 3 cos wt is applied to the system. (i) Assuming the damping force in pounds is numerically equal to 4(dx/dt), where dx/dt is the instantaneouse velocity in feet per second, find the displacement as a function of the time and determine the resonance frequency of resulting motion. (ii) (ii) Assuming there is no damping, determine the value of w which gives rise to undamped resonance.
Transcribed Image Text:A 64 lb weight is attached to the lower end of a coil spring suspended from the ceiling, the spring constant being 18 lb/ft. The weight comes to rest in its equilibrium position. It in then pulled down 6 inches below its equilibrium position and released at t = 0. At this instant, an external force given by F(t) = 3 cos wt is applied to the system. (i) Assuming the damping force in pounds is numerically equal to 4(dx/dt), where dx/dt is the instantaneouse velocity in feet per second, find the displacement as a function of the time and determine the resonance frequency of resulting motion. (ii) (ii) Assuming there is no damping, determine the value of w which gives rise to undamped resonance.
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