The simple harmonic oscillator (SHO) is probably the single most important approximation for describing small displacements...

The simple harmonic oscillator (SHO) is probably the single most important approximation for describing small displacements about stable equilibrium positions. Why is it that the SHO approximation actually works? What are the limitations of the SHO?

Expert Solution

genius_generous answered 2 years ago

7. Consider two noninteracting particles in a 1D simple harmonic oscillator (SHO) potential, which has 1-particle...

7. Consider two noninteracting particles in a 1D simple harmonic oscillator (SHO) potential, which has 1-particle spatial wavefunctions ψ n ( x), where n = 0, 1, 2, … (we ignore spin by assuming both particles have the same spin quantum number or are spin 0). These wavefunctions are normalized to 1 and satisfy ψ n * ( x)ψ m ( x)dx −∞ ∞ ∫ = 0 when n ≠ m , i.e., they are orthogonal. The energies are !ω0...

Demonstrate that the WKB approximation yields the energy levels of the linear harmonic oscillator and compute...

Demonstrate that the WKB approximation yields the energy levels of the linear harmonic oscillator and compute the WKB approximation for the energy eigenfunctions for the n=0 and n=1 state and compute with the exact stationary state solutions.

Method A: Based on the frequency of a simple harmonic oscillator. The angular frequency of a...

Method A: Based on the frequency of a simple harmonic oscillator. The angular frequency of a mass on a spring is given by ω=(k/m)1/2ω=(k/m)1/2 where m is the mass and k is the spring constant. The period of a harmonic oscillator is T=2π/ωT=2π/ω . If you do a little math, you can get a formula for the spring constant in terms of the mass and the period. a) Design a procedure to measure the spring constant based on Method A...

As in the figure below, a simple harmonic oscillator is attached to a rope of linear...

As in the figure below, a simple harmonic oscillator is attached to a rope of linear mass density 5.4 ✕ 10−2 kg/m, creating a standing transverse wave. There is a 3.5-kg block hanging from the other end of the rope over a pulley. The oscillator has an angular frequency of 44.1 rad/s and an amplitude of 255.0 cm. (a) What is the distance between adjacent nodes? m (b) If the angular frequency of the oscillator doubles, what happens to the...

a) a simple harmonic oscillator consists of a glass bead attached to a spring. it is...

a) a simple harmonic oscillator consists of a glass bead attached to a spring. it is immersed in a liquid where it loses 10% of its energy over 10 periods. compute the coefficient of kinetic friction b assuming spring constant k=1 N/m and mass m=10 grams; b) suppose the spring is now disconnected and the bead starts failing in the liquid, accelerating until it reaches the terminal velocity. compute the terminal velocity.

Quantum Mechanics Determine the settlement approach (approximation) for the harmonic oscillator system due to the relativistic...

Quantum Mechanics Determine the settlement approach (approximation) for the harmonic oscillator system due to the relativistic term using the perturbation method in order 2 correction.

1. (a) Describe in your own words and mathematically the harmonic oscillator approximation to molecular vibration....

1. (a) Describe in your own words and mathematically the harmonic oscillator approximation to molecular vibration. (b) What does this approximation lack in terms of representing real molecular bonds? (c) When is the approximation most valid and when are higher order approximations necessary?

The displacement as a function of time of a 4.0kg mass spring simple harmonic oscillator is...

The displacement as a function of time of a 4.0kg mass spring simple harmonic oscillator is . What is the displacement of the mass at 2.2 seconds? ___________m What is the spring constant? ___________________N/m What is the position of the object when the speed is maximum? ______________m What is the magnitude of the maximum velocity?____________________m/s

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...

1. A simple harmonic oscillator consists of a block of mass 4.20 kg attached to a...

1. A simple harmonic oscillator consists of a block of mass 4.20 kg attached to a spring of spring constant 290 N/m. When t = 2.10 s, the position and velocity of the block are x = 0.141 m and v = 3.530 m/s. (a) What is the amplitude of the oscillations? What were the (b) position and (c) velocity of the block at t = 0 s? 2. If you took your pendulum to the moon, where the acceleration...

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