A 10 10 kilogram object suspended from the end of a vertically hanging spring stretches the...

A 10 10 kilogram object suspended from the end of a vertically hanging spring stretches the spring 9.8 9.8 centimeters. At time ?=0 t = 0 , the resulting mass-spring system is disturbed from its rest state by the force ?(?)=70cos(8?) F ( t ) = 70 cos ( 8 t ) . The force ?(?) F ( t ) is expressed in Newtons and is positive in the downward direction, and time is measured in seconds.

a) Determine the spring constant ?.

b) Formulate the initial value problem for ?(?)y(t), where ?(?)y(t) is the displacement of the object from its equilibrium rest state, measured positive in the downward direction. (Give your answer in terms of ?,?′,?′′,?y,y′,y′′,t.)

c) Solve the initial value problem for ?(?)y(t).

Solutions

Expert Solution

Hope you liked it

Pls like it

Colby Messinger answered 1 year ago

Next > < Previous

Related Solutions

A 2.5kg object oscillates at the end of a vertically hanging light spring once every 0.65s...

A 2.5kg object oscillates at the end of a vertically hanging light spring once every 0.65s . Part A Write down the equation giving its position y (+ upward) as a function of time t. Assume the object started by being compressed 17cm from the equilibrium position (where y = 0), and released. Write down the equation giving its position ( upward) as a function of time . Assume the object started by being compressed 17 from the equilibrium position (where =...

2. A 6-lb weight is attached to a vertically suspended spring that it stretches 4 in....

2. A 6-lb weight is attached to a vertically suspended spring that it stretches 4 in. and to adashpot that provides 1.5 lb of resistance for every foot per second of velocity.(a) If the weight is pulled down 1 ft below its static equilibrium position and then released from rest at time t = 0, find its position function .(b) Find the frequency, time-varying amplitude, and phase angle of the motion.(Give exact answers for both parts.

A 8.50 kg mass is attached to the end of a hanging spring and stretches it...

A 8.50 kg mass is attached to the end of a hanging spring and stretches it 28.0 cm. It is then pulled down an additional 12.0 cm and then let go. What is the maximum acceleration of the mass? At what position does this occur? What is the position and velocity of the mass 0.63 s after release?

1. Assume that hanging a 100 gram mass from a given spring stretches the spring by...

1. Assume that hanging a 100 gram mass from a given spring stretches the spring by 2 cm. If two springs of this kind are connected back to back (series configuration), how much would the combination stretch if a 200 gram mass is suspended? a. 1 cm b. 2 cm c. 3 cm d. 4 cm e. none of these 2. What would be the answer to the previous question if the two springs were connected in parallel configuration? a....

You have a spring hanging vertically. You add a mass to the end and let it...

You have a spring hanging vertically. You add a mass to the end and let it stretch to find its new equilibrium position which is 3.17 cm below the unstretched position. You now raise the mass (compress the mass-spring system) to its original unstretched position. Now you release the mass. How far from this starting position does it travel downward until it stops and changes direction?

When a body of mass 1.0 kg is suspended from a certain light spring hanging vertically, its length increases by 5 cm

When a body of mass 1.0 kg is suspended from a certain light spring hanging vertically, its length increases by 5 cm. By suspending 2.0 kg block to the spring and if the block is pulled through 10 cm and released, the maximum velocity of it in m/s is approximately

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 spring constant of 250.0 N/m is suspended vertically with its upper end fixed to the...

A spring constant of 250.0 N/m is suspended vertically with its upper end fixed to the ceiling and its lower end at position y=0.000 cm. A block of weight 25.0 N is attached to the lower end, held still for a moment and then released. What are the kinetic energy changes and the changes from initial values in the gravitational potential energy of the spring-block system when the block is at values of y equal to (a) -5.00 cm (b)...

A 0.167-kg frame, when suspended from a coil spring, stretches the spring 0.0400 m. A 0.200-kg...

A 0.167-kg frame, when suspended from a coil spring, stretches the spring 0.0400 m. A 0.200-kg lump of putty is dropped from rest onto the frame from a height of 30.0 cm. Find the maximum distance the frame moves downward from its initial equilibrium position.

(1 point) A hollow steel ball weighing 4 pounds is suspended from a spring. This stretches...

(1 point) A hollow steel ball weighing 4 pounds is suspended from a spring. This stretches the spring 1/6 feet. The ball is started in motion from the equilibrium position with a downward velocity of 4 feet per second. The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet per second) . Suppose that after t seconds the ball is y feet below its rest position. Find y in terms of t. (Note...

Subjects