A 30-pound mass of weight stretches a spring to a 10-foot spring, if the medium surrounding...

A 30-pound mass of weight stretches a spring to a 10-foot spring, if the medium surrounding the system has a damping coefficient, that is, it is equivalent to 5 times the instantaneous speed and the weight is released from a point located at 16 inches below equilibrium position with an initial velocity of 1 foot per second down. A) Deduce the Differential Equation that models the mass-spring system. b) Calculate the displacements (t) at all times t.

Expert Solution

genius_generous answered 2 years ago

1. An 8 pound weight stretches a spring 2 feet. The surrounding medium offers a damping...

1. An 8 pound weight stretches a spring 2 feet. The surrounding medium offers a damping force that is numerically equal to 2 times the instantaneous velocity. It is then released from rest from a point 3 feet below the equilibrium point. a. Determine the equation of motion. b. Is the system underdamped, overdamped, or critically damped?

A 16-lb weight stretches a spring 16 ft. The spring-mass system is in a medium with...

A 16-lb weight stretches a spring 16 ft. The spring-mass system is in a medium with a damping constant of 1.5 lb-sec/ft, and an external force given by f (t)= 3+e^-3t (in pounds) is being applied. What is the solution function describing the position of the mass at any time of the mass is released from 1ft below the equilibrium position with an initial velocity of 2 ft/sec downward?

An 8-pound weight is attached to a spring hanging from a ceiling. The weight stretches the...

An 8-pound weight is attached to a spring hanging from a ceiling. The weight stretches the spring 9.6 inches, coming to rest at its stretched equilibrium position. The weight is displaced 8 inches below this stretched equilibrium position, and at time t = 0 the mass is released. At the same instant, an external force of F(t)= 2cos(2t) pounds is applied to the system. The damping constant is 1 lb/(ft/sec). Find the function that gives the displacement of the mass...

A mass of 1.5 kg stretches a spring 0.05 mm. The mass is in a medium...

A mass of 1.5 kg stretches a spring 0.05 mm. The mass is in a medium that exerts a viscous resistance of 240 NNwhen the mass has a velocity of 6 msms. The viscous resistance is proportional to the speed of the object. Suppose the object is displaced an additional 0.06 mm and released. Find an function to express the object's displacement from the spring's natural position, in mm after tt seconds. Let positive displacements indicate a stretched spring, and...

Consider a mass-spring system with an iron ball (weight 16 pound force) that stretches 8/9 ft...

Consider a mass-spring system with an iron ball (weight 16 pound force) that stretches 8/9 ft with undamped motion. The spring is initially displaced 6 inches upwards from its equilibrium position and given an initial velocity of 1 ft/s downward. Assume the relation mg=hk. a. Find the displacement at any time t. b. Find the natural frequency of the mass-spring (i.e. iron ball-spring) system. c. How many cycles per minutes will the system execute? d. What would be the amplitude...

A mass that weight 5lb stretches a spring 3in. The system is acted on by an...

A mass that weight 5lb stretches a spring 3in. The system is acted on by an external force 6sin⁡(8sqrt2 t)lb. If the mass is pulled down 4in and then released, determine the position of the mass at any time t. Use 32ft/s2 as the acceleration due to gravity. Pay close attention to the units. u(t)=

A mass that weight 15lb15lb stretches a spring 8in8in. The system is acted on by an...

A mass that weight 15lb15lb stretches a spring 8in8in. The system is acted on by an external force 9sin(43–√t)lb9sin⁡(43t)lb.If the mass is pulled down 3in3in and then released, determine the position of the mass at any time tt. Use 32ft/s232ft/s2 as the acceleration due to gravity. Pay close attention to the units. Answer must be in inches

A mass that weight 6lb stretches a spring 4in. The system is acted on by an...

A mass that weight 6lb stretches a spring 4in. The system is acted on by an external force 2sin(4sqrt(6)t)lb.If the mass is pulled down 3in and then released, determine the position of the mass at any time t. Use 32ft/s^2 as the acceleration due to gravity. Pay close attention to the units. Answer must be in inches

A mass weighing 8 pounds stretches a spring 1 foot. The mass is initially released from...

A mass weighing 8 pounds stretches a spring 1 foot. The mass is initially released from rest from a point 2 feet below the equilibrium position, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to 2 times the instantaneous velocity. Find the equation of motion (solve the IVP) if the mass is driven by an external force equal to f(t) = 5 cos(2t). Graph the solution. What part of the...

A mass weighing 8 lb stretches a spring 1/2 foot. Then mass is initially released from...

A mass weighing 8 lb stretches a spring 1/2 foot. Then mass is initially released from rest at a point 1 foot above the equilibrium. a) Solve the equation of motion with no damping. Use the same spring system and initial conditions as in Problem above. The spring system is now placed in a medium that offers a damping force equal to 2 times the instantaneous velocity. b) Solve the equation of motion c) At what time does the mass...

Question