A force of 540 newtons stretches a spring 3 meters. A mass of 45 kilograms is attached to the end of the spring

PLEASE ANSWER ALL 3 WILL THUMBS UP

1) A force of 540 newtons stretches a spring 3 meters. A mass of 45 kilograms is attached to the end of the spring and is initially released from the equilibrium position with an upward velocity of 8 m/s. Find the equation of motion.

x(t)=? m

2) Find the charge on the capacitor and the current in an LC-series circuit when L = 0.1 h, C = 0.1 f, E(t) = 100 sin(γt) V, q(0) = 0 C, and i(0) = 0 A

q(t)= ?

i(t)= ?

3) Find the steady state current i_p(t) in an LRC-series circuit when L = 1/2 h, R= 20 ohms, C= 0.001 f and E(t) = 400sin(60t)+500cos(40t) V

i_p(t)= ?

Solutions

Expert Solution

Colby Messinger answered 1 year ago

Next > < Previous

Related Solutions

A force of 640 newtons stretches a spring 4 meters. A mass of 40 kilograms is...

A force of 640 newtons stretches a spring 4 meters. A mass of 40 kilograms is attached to the end of the spring and is initially released from the equilibrium position with an upward velocity of 10 m/s. Find the equation of motion.

A force of 720 Newton stretches a spring 4 meters. A mass of 45 Kilograms is...

A force of 720 Newton stretches a spring 4 meters. A mass of 45 Kilograms is attached to the spring and is initially released from the equilibrium position with an upward velocity of 6 meters per second. Find an equation of the motion.

A force of 400N stretches a spring 2m. A mass of 50kg is attached to the...

A force of 400N stretches a spring 2m. A mass of 50kg is attached to the end of the spring and put in a viscous fluid with a damping force that is 100 times the instantaneous velocity. The mass is released from the equilibrium position with a downward velocity of 1m/s. (a) Determine the natural frequency of the system. (b) Determine the level of damping in the system. (c) Write the differential equation of motion (d) Solve the system and...

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)A force of 2 N stretches a spring 0.5 meters. The mass of 1 kg is...

1)A force of 2 N stretches a spring 0.5 meters. The mass of 1 kg is attached to the spring and set into motion in a medium that offers a damped force equal 4 times the velocity. If the mass is at stating from 0.5 m above the equilibrium position with a downward initial velocity of sec/2.0m a) Find the equation for the position if the system is exerted by an external force of f(t)=4cos(t) b)Estimate the position of the...

1) When a mass of 3 kilograms is attached to a spring whose constant is 48...

1) When a mass of 3 kilograms is attached to a spring whose constant is 48 N/m, it comes to rest in the equilibrium position. Starting at t = 0, a force equal to f(t) = 180e−4t cos(4t) is applied to the system. Find the equation of motion in the absence of damping. x(t) = 2) Solve the given initial-value problem. d^(2)x/dt^2 + 9x = 5 sin(3t), x(0) = 6, x'(0) = 0 x(t) =

A mass weighing 17 lb stretches a spring 7 in. The mass is attached to a...

A mass weighing 17 lb stretches a spring 7 in. The mass is attached to a viscous damper with damping constant 2 lb *s/ft. The mass is pushed upward, contracting the spring a distance of 2 in, and then set into motion with a downward velocity of 2 in/s. Determine the position u of the mass at any time t. Use 32 ft/s^2 as the acceleration due to gravity. Pay close attention to the units. Leave answer in terms of...

a mass weighing 10 newtons stretches a spring 10/49m. the mass is releases from 6 m...

a mass weighing 10 newtons stretches a spring 10/49m. the mass is releases from 6 m below equilibrium with a downward velocity of 42 m/s in a median which offers a damping force numerically equal to 14 times the instantaneous velocity. use g=10m^2/s. (a) Find the equation of motion. y(t) = m. (b) find the time when the spring reaches its maximum displacement.

A mass of 20 grams stretches a spring 5cm. Suppose that the mass is also attached...

A mass of 20 grams stretches a spring 5cm. Suppose that the mass is also attached to a damper with constant coefficient 0.4 N·s/m. Initially the mass is pulled down an additional 2cm and released. Write a differential equation for the position u(t) of the mass at time t (make the units meters, kilograms, Newtons, seconds). Do NOT solve the differential equation. The solution to a differential equation that models a vibrating spring is u(t) = 4e−t cos(3t) + 3e−t...

A mass weighing 12lb stretches a spring 10in.. The mass is attached to a viscous damper...

A mass weighing 12lb stretches a spring 10in.. The mass is attached to a viscous damper with damping constant 3lb*s/ft. The mass is pushed upward, contracting the spring a distance of 2in, and then set into motion with a downward velocity of 4in/s. Determine the position of the mass at any time . Use as 32ft/s^2the acceleration due to gravity. Pay close attention to the units.

Subjects