A mass weighting 40 lbs stretches a spring 3 inches. The mass is in a medium that exerts a viscous resistance of 10 lbs when the mass has a velocity of 2 ft/sec. Suppose the object is displaced an additional 4 inches and released. Find an equation for the object's displacement, u(t), in feet after t seconds.
A mass weighting 40 lbs stretches a spring 3 inches. The mass is in a medium that exerts a viscous resistance of 10 lbs when the mass has a velocity of 2 ft/sec. Suppose the object is displaced an additional 4 inches and released. Find an equation for the object's displacement, u(t), in feet after t seconds.
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Step 1: Determine the given data:
VIEWStep 2: Calculation of constant of viscous resistance:
VIEWStep 3: Calculation of stiffness constant of spring:
VIEWStep 4: Write the differential equation of motion:
VIEWStep 5: Determine the general solution:
VIEWStep 6: Apply the boundary conditions to calculate final equation of motion u(t):
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