mass of 1.75 kg is attached to the end of a spring whose restoring force is 100 N/m. The mass is in a medium that exerts a viscous resistance of 15 N when the mass has a velocity of 6 msms. The viscous resistance is proportional to the speed of the object. Suppose the spring is stretched 0.03 mm beyond the its natural position and released. Let positive displacements indicate a stretched spring, and suppose that external vibrations act on the mass with a force of 3sin(2t) NN at time tt seconds. Find an function to express the steady-state component of the object's displacement from the spring's natural position, in mm after tt seconds. (Note: This spring-mass system is not "hanging", so there is no gravitational force included in the model.) Enter exact value for the constants, or 8 decimal places.
A mass of 1.75 kg is attached to the end of a spring whose restoring force is 100 N/m. The mass is in a medium that exerts a viscous resistance of 15 N when the mass has a velocity of 6 msms. The viscous resistance is proportional to the speed of the object.
Suppose the spring is stretched 0.03 mm beyond the its natural position and released. Let positive displacements indicate a stretched spring, and suppose that external vibrations act on the mass with a force of 3sin(2t) NN at time tt seconds.
Find an function to express the steady-state component of the object's displacement from the spring's natural position, in mm after tt seconds. (Note: This spring-mass system is not "hanging", so there is no gravitational force included in the model.)
Enter exact value for the constants, or 8 decimal places.
u(t) =
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