a. A 0.5 kg mass attached to a linear spring, with spring constant 5 N/m and...

a. A 0.5 kg mass attached to a linear spring, with spring constant 5 N/m and damping constant 0.2 kg/s, is initially displaced 10 cm from equilibrium. (a) What is the natural frequency of oscillation? What is its period of oscillation? How long does it take for the amplitude to decrease to 10% of its starting value? How many oscillations have occurred in this time? What fraction of the initial energy remains after this time?

b. Two traveling waves with the same amplitude A, frequency f, and wavelength λ, but out of phase with each other by one quarter of a wavelength, are both traveling to the right and superpose in space. Find the amplitude, wavelength, and frequency of the resulting wave in terms of the given symbols. Write the equation of the resulting traveling wave y ( x , t ).

Expert Solution

This is the Question of damping wave oscillation which can be solved using damping wave equation.

genius_generous answered 1 year ago

A 0.5-kg mass is attached to a spring with spring constant 2.5 N/m. The spring experiences...

A 0.5-kg mass is attached to a spring with spring constant 2.5 N/m. The spring experiences friction, which acts as a force opposite and proportional to the velocity, with magnitude 2 N for every m/s of velocity. The spring is stretched 1 meter and then released. (a) Find a formula for the position of the mass as a function of time. (b) How much time does it take the mass to complete one oscillation (to pass the equilibrium point, bounce...

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

1. A mass of 0.019 kg attached to a spring with spring constant 27.0 N/m is...

1. A mass of 0.019 kg attached to a spring with spring constant 27.0 N/m is pulled to the right 8.0 cm and released. The mass oscillates with a frequency of 6.0 Hz. If the mass is pulled to the right 16.0 cm before being released, what is the frequency? a. 6.0 Hz b. 3.0 Hz c. 1.5 Hz d. 12 Hz e. 24 Hz 2. A window loses power/heat energy through a pane of glass to the cold outside....

A block of mass m = 2.5 kg is attached to a spring with spring constant...

A block of mass m = 2.5 kg is attached to a spring with spring constant k = 640 N/m. It is initially at rest on an inclined plane that is at an angle of θ = 27° with respect to the horizontal, and the coefficient of kinetic friction between the block and the plane is μk = 0.11. In the initial position, where the spring is compressed by a distance of d = 0.19 m, the mass is at...

a block of mass m=0.10 kg attached to a spring whose spring constant is k=2.5 N/m...

a block of mass m=0.10 kg attached to a spring whose spring constant is k=2.5 N/m . At t=0.2s, the displacement x=-0.3m, and the velocity v=-2.0m/s a) find the equation of displacement as a function of time b) sketch the displacement as a function of time for the first cycle starting t=0s

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?

A 0.770-kg mass attached to a vertical spring of force constant 147 N/m oscillates with a...

A 0.770-kg mass attached to a vertical spring of force constant 147 N/m oscillates with a maximum speed of 0.322 m/s. Calculate the period related to the motion of the mass. Calculate the amplitude. Calculate the maximum magnitude of the acceleration.

A mass m = 3.27 kg is attached to a spring of force constant k =...

A mass m = 3.27 kg is attached to a spring of force constant k = 60.9 N/m and set into oscillation on a horizontal frictionless surface by stretching it an amount A = 0.17 m from its equilibrium position and then releasing it. The figure below shows the oscillating mass and the particle on the associated reference circle at some time after its release. The reference circle has a radius A, and the particle traveling on the reference circle...

A mass m = 1 kg is attached to a spring with constant k = 4...

A mass m = 1 kg is attached to a spring with constant k = 4 N/m and a dashpot with variable damping coefficient c. If the mass is to be pulled 5 m beyond its equilibrium (stretching the spring) and released with zero velocity, what value of c ensures that the mass will pass through the equilibrium position and compress the spring exactly 1 m before reversing direction? c =

Question