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) =

Solutions

Expert Solution

Colby Messinger answered 1 year ago

Next > < Previous

Related Solutions

When a 5 kg mass is attached to a spring whose constant is 180 N/m, it...

When a 5 kg mass is attached to a spring whose constant is 180 N/m, it comes to rest in the equilibrium position. Starting at t = 0, a force equal to f (t) = 20e−3t cos 6t is applied to the system. In the absence of damping, (a) find the position of the mass when t = π. (b) what is the amplitude of vibrations after a very long time

When a 6 kg mass is attached to a spring whose constant is 24 N/m, it...

When a 6 kg mass is attached to a spring whose constant is 24 N/m, it comes to rest in the equilibrium position. Starting at t = 0, a force equal to f (t) = 42e−7t cos 4t is applied to the system. In the absence of damping, (a) find the position of the mass when t = π. (b) what is the amplitude of vibrations after a very long time?

When a 6 kg mass is attached to a spring whose constant is 294 N/m, it...

When a 6 kg mass is attached to a spring whose constant is 294 N/m, it comes to rest in the equilibrium position. Starting at t = 0, a force equal to f (t) = 12e−4t cos 3t is applied to the system. In the absence of damping, (a) find the position of the mass when t = π. (b) what is the amplitude of vibrations after a very long time?

The displacement of a block of mass 1.280 kg attached to a spring whose spring constant...

The displacement of a block of mass 1.280 kg attached to a spring whose spring constant is 50 N/m is given by x = A cos ωt, where A = 12 cm. In the first complete cycle, find the values of x and t at which the kinetic energy is equal to one half the potential energy.

A 1-kilogram mass is attached to a spring whose constant is 16 N/m, and the entire...

A 1-kilogram mass is attached to a spring whose constant is 16 N/m, and the entire system is then submerged in a liquid that imparts a damping force numerically equal to 10 times the instantaneous velocity. The mass is initially released from rest from a point 1 meter below the equilibrium position. 1. Show the Diagram, given and required only ( No need to solve, Thumbs up will only be given if 1 is followed.)

1. A 1 kilogram mass is attached to a spring with a spring constant of 4...

1. A 1 kilogram mass is attached to a spring with a spring constant of 4 N/m. Write the equation of motion if the spring is stretched 25 cm below the equilibrium position and released. a) Suppose the system experiences a constant forcing function downwards of 4 N. (Note that one would need to divide by the mass, but the mass is 1 kg so we don’t see a difference here.) Solve the non-homogeneous equation. (Keep everything else about the...

A vertical spring (ignore its mass), whose spring constant is 825 N/m , is attached to...

A vertical spring (ignore its mass), whose spring constant is 825 N/m , is attached to a table and is compressed down by 0.160 m. A)What upward speed can it give to a 0.360-kg ball when released? Express your answer to three significant figures and include the appropriate units. B) How high above its original position (spring compressed) will the ball fly? Express your answer to three significant figures and include the appropriate units.

A mass of 2 kilogram is attached to a spring whose constant is 8 N/m, and...

A mass of 2 kilogram is attached to a spring whose constant is 8 N/m, and the entire system is then submerged in a liquid that imparts a damping force equal to 8 times the instantaneous velocity. At t = 0 the mass is released from the equilibrium position with no initial velocity. An external force f(t) = 2U(t−1)*e^(−2(t−1)) is applied. (a) Write f(t), the external force, as a piecewise function and sketch its graph. (b) Write the initial-value problem....

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)...

spring-mass system has a spring constant of 3 Nm. A mass of 2 kg is attached...

spring-mass system has a spring constant of 3 Nm. A mass of 2 kg is attached to the spring, and the motion takes place in a viscous fluid that offers a resistance numerically equal to the magnitude of the instantaneous velocity. If the system is driven by an external force of 15cos(3t)−10sin(3t) N,determine the steady-state response in the form Rcos(ωt−δ). R= _________ ω=__________ δ=___________

Subjects