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

Expert Solution

Colby Messinger answered 1 month ago

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 7kg of stretches a spring 18cm. The mass is acted on by an external...

A mass 7kg of stretches a spring 18cm. The mass is acted on by an external force of 5sin(t/2) N and moves in a medium that imparts a viscous force of 4N when the speed of the mass is 8cm/s. If the mass is set in motion from its equilibrium position with an initial velocity of 4cm/s, determine the position of the mass at any time t. Use 9.8m/s2 as the acceleration due to gravity. Pay close attention to the...

A mass of 8 kg stretches a spring 16 cm. The mass is acted on by...

A mass of 8 kg stretches a spring 16 cm. The mass is acted on by an external force of 7sin⁡(t/4)N and moves in a medium that imparts a viscous force of 3 N when the speed of the mass is 6 cm/s.If the mass is set in motion from its equilibrium position with an initial velocity of 4 cm/s, determine the position u of the mass at any time t. Use 9.8 m/s^2 as the acceleration due to gravity....

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?

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.

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 1-kg mass stretches a spring 20 cm. The system is attached to a dashpot that...

A 1-kg mass stretches a spring 20 cm. The system is attached to a dashpot that imparts a damping force equal to 14 times the instantaneous velocity of the mass. Find the equation of motion if the mass is released from equilibrium with an upward velocity of 3 m/sec. SOLVE THIS USING MATLAB CODE (SECOND ORDER DIFFERENTIAL EQUATIONS) SOLVE THIS USING MATLAB CODE (SECOND ORDER DIFFERENTIAL EQUATIONS) SOLVE THIS USING MATLAB CODE (SECOND ORDER DIFFERENTIAL EQUATIONS) SOLVE THIS USING MATLAB...

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 50 g stretches a spring 3.828125 cm. If the mass is set in...

A mass of 50 g stretches a spring 3.828125 cm. If the mass is set in motion from its equilibrium position with a downward velocity of 50 cms, and if there is no damping, determine the position u of the mass at any time t. Enclose arguments of functions in parentheses. For example, sin(2x). Assume g=9.8 ms2. Enter an exact answer. u(t)= m When does the mass first return to its equilibrium position? Enter an exact answer. t= s

Question