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 sin(3t) + 51 cos(2t) + 25 sin(2t) .

(b) Determine the transient part of the solution.
(c) Determine the phase, quasi-amplitude, quasi-frequency, quasi-period. (d) Determine the steady state part of the solution.
(e) Determine the phase, amplitude, frequency, period. of the steady part of the solution.

Expert Solution

genius_generous answered 1 year ago

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...

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 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?

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.

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 u 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 attached to a spring is displaced from its equilibrium position by 5cm and released....

A mass attached to a spring is displaced from its equilibrium position by 5cm and released. The system then oscillates in simple harmonic motion with a period of 1s. If that same mass–spring system is displaced from equilibrium by 10cm instead, what will its period be in this case? A mass attached to a spring is displaced from its equilibrium position by and released. The system then oscillates in simple harmonic motion with a period of . If that same mass–spring...

A mass of 1 slug, when attached to a spring, stretches it 2 feet. It is...

A mass of 1 slug, when attached to a spring, stretches it 2 feet. It is released from a point 1 foot above the equilibrium position with a downward velocity of 2 ft/s. 1) Find the equation of motion if the surrounding medium offers a damping force that is numerically equal to 4 times the instantaneous velocity. 2) Classify the motion as underdamped, overdamped, or critically damped.

A mass of 1 slug, when attached to a spring, stretches it 2 feet and then...

A mass of 1 slug, when attached to a spring, stretches it 2 feet and then comes to rest in the equilibrium position. Starting at t = 0, an external force equal to f(t) = 10 sin(4t) is applied to the system. Find the equation of motion if the surrounding medium offers a damping force that is numerically equal to 8 times the instantaneous velocity. (Use g = 32 ft/s2 for the acceleration due to gravity.) x(t) = ____________ft

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)...

Question