Derive the Kramers-Kronig relation for a damped harmonic oscillator. The parameters can be chosen randomly.

Expert Solution

genius_generous answered 2 years ago

1.For a damped simple harmonic oscillator, the block has a mass of 2.3 kg and the...

1.For a damped simple harmonic oscillator, the block has a mass of 2.3 kg and the spring constant is 6.6 N/m. The damping force is given by -b(dx/dt), where b = 220 g/s. The block is pulled down 12.4 cm and released. (a) Calculate the time required for the amplitude of the resulting oscillations to fall to 1/8 of its initial value. (b) How many oscillations are made by the block in this time? 2.An oscillator consists of a block...

Please provide an example of a damped harmonic oscillator. They are more common than undamped or...

Please provide an example of a damped harmonic oscillator. They are more common than undamped or simple harmonic oscillators. What do you think there is any harmonic motion in the physical world that is not damped harmonic motion? Try to make a list of five examples of undamped harmonic motion and damped harmonic motion. Which list was easier to make? Why are the group of the peoples in general ordered to “route step” (walk out of step) across a bridge?

For a damped harmonic oscillator m = 200 g k = 45 N/m and b =...

For a damped harmonic oscillator m = 200 g k = 45 N/m and b = 70 g/s. What is the periodic time of the motion in seconds?

consider a linearly damped simple harmonic oscillator with mass m,restoring force contsant k and resistive force...

consider a linearly damped simple harmonic oscillator with mass m,restoring force contsant k and resistive force constant c.if c >sqrt(4mk), work out the expression for the displacement as a function of time and describe the predicted time dependence of the motion.

(10pts) Consider the damped forced harmonic oscillator with mass 1 kg, damping coefficient 2, spring constant...

(10pts) Consider the damped forced harmonic oscillator with mass 1 kg, damping coefficient 2, spring constant 3, and external force in the form of an instantaneous hammer strike (Section 6.4) at time t = 4 seconds. The mass is initially displaced 2 meters in the positive direction and an initial velocity of 1 m/s is applied. Model this situation with an initial value problem and solve it using the method of Laplace transforms.

This problem is an example of critically damped harmonic motion.

This problem is an example of critically damped harmonic motion. A mass m=6kg is attached to both a spring with spring constant k=96N/m and a dash-pot with damping constant c=48N⋅s/m . The ball is started in motion with initial position x0=5m and initial velocity v0=−24m/s . Determine the position function x(t) in meters. x(t)= Graph the function x(t) . Now assume the mass is set in motion with the same initial position and velocity, but with the dashpot disconnected (...

The vibrations of a bi-atomic molecule AB can be approximated as a harmonic oscillator with the...

The vibrations of a bi-atomic molecule AB can be approximated as a harmonic oscillator with the potential energy of type V (x) = (kx^2)/2, x representing the spatial deviation of the relative position between those 2 molecules towards equilibrium. Calculate the vibrational energy of the H2 molecule knowing that k = 510N/m and the mass of a hydrogen atom is m0 = 1.66 ∗ 10−27 kg

1. A damped driven harmonic oscillator with m=12 kg, k=280 N/m, and b=75 kg/sis subjected to...

1. A damped driven harmonic oscillator with m=12 kg, k=280 N/m, and b=75 kg/sis subjected to a driving force given by F(t) = F0cos(ωt), where F0=55 N. a) What value of ω results in steady-state oscillations with maximum amplitude? b) What is the maximum amplitude? c) What is the phase angle? 2. An undamped, driven harmonic oscillator satisfies the equation of motion where the driving force is switched on at t=0. a) Assuming a solution of the form x(t) =...

Explain why in the case of the quantum harmonic oscillator the wave function can cross the...

Explain why in the case of the quantum harmonic oscillator the wave function can cross the potential barrier and why does the same not happen in the case of the infinite potential well? Explain in detail

1) What is ? for a harmonic oscillator (in terms of the period)?

1) What is ? for a harmonic oscillator (in terms of the period)? 2) What is ? for a spring? A) If you increase the amplitude, what happens to the period? B) If you increase the mass, what happens to the period? C) If you increase the spring constant, what happens to the period? 3) What is ? for a simple pendulum? A) If you increase the amplitude, what happens to the period? B) If you increase the mass,...

Question