The restoring force of an anharmonic oscillator is proportional to the cube of the displacement. Show that

Question:

The restoring force of an anharmonic oscillator is proportional to the cube of the displacement. Show that the mean kinetic energy of the oscillator is twice its mean potential energy.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For answer-question

Statistical Mechanics

ISBN: 9780123821881

3rd Edition

Authors: Paul D. Beale

See More Books

Question Posted: Mar 16, 2024 07:00 AM

See More Questions

16) A company purchases machinery for $10,000. It also spends $800 to ship it to its location, $600 to unpack and install it, $500 to test and debug it, and $300 to fix a crack caused by an accident...
The potential for an anharmonic oscillator is U = kx2/2 + bx4/4 where k and b are constants. Find Hamiltons equation of motion.
In Problem 19, what is a differential equation for the displacement x(t) if the motion takes place in a medium that imparts a damping force on the spring/ mass system that is proportional to the...
Would individual mandates for health insurance be more or less burdensome to the poor than employer mandates? Would lower-income groups be wise to favor one plan over the other?
Why does a motor also tend to act as a generator?
A capacitor with capacitance C whose interelectrode space is filled up with poorly conducting medium with active resistance R is connected to a source of alternating voltage V = Vm cos cot. Find the...
Repeat Example 7.3 using $10 \mathrm{~kg} / \mathrm{h}$ of solvent in each stage. Data From Example 7.3:- The feed of Example 7.2 is extracted three times with pure chloroform at 298 K, using 8...
In preparation for significant international operations, ABC Co. has adopted a plan to gradually shift to the same accounting methods as used by its international competitors. Part of this plan...
Table 17-4 Features of alternative security issues Common Stock Preferred Stock Bonds 1.Ownership and control of the firm Belongs to common stockholders through voting rights and residual claim to...
Derive the virial equation of state equation (3.7.15) from the classical canonical partition function (3.5.5). Show that in the thermodynamic limit the interparticle terms dominate the ones that come...
(a) Calculate the time-averaged kinetic energy and potential energy of a one-dimensional harmonic oscillator, both classically and quantum-mechanically, and show that the results obtained are...
What are the major functions of a reporting system?
A long - sighted eye has a near point at 0 . 5 0 m away. Calculate the power of the correcting lens to give a corrected near point at 2 5 cm from the eye.
You have been asked to evaluate the investment opportunity for a company your firm would like to invest in. From all the available data that you have compiled, you have summarized the following...
Use MATLAB to solve the following: Consider the random variable X = [(Ui - 12) 12 i=1, where the Ut's are uniform random variables. 6.1 Write a MATLAB code to estimate (use 1,000 trials) the PDF...
You get a job in the mortgage-backed security department at Moodys, a rating agency. The model you are given states that mortgage defaults are independent events. You are asked to rate the following...
Use the linear equation to find the estimated top speed of a rollercoaster based on a max height of 190 ft. Must show work or no credit. Name Max Height Top Speed Blue Streak 78 40 Iron Dragon 76 40...
A long horizontal wire carries a current a of 48 A.A second wire, made of 2.5-mm-diameter copper wire and parallel to the first, is kept in suspension magnetically 15 cm below (Fig. 20-58). (a)...
[a] Two foam blocks, each with a charge of 19 micro coulombs (1 C = 10-6 C), are both held in place 19 cm apart in the east-west direction. A foam ball with a charge 49 C is placed 55 cm north of the...
A particle moves with a cylindrically symmetric potential energy $U=U(ho, z)$ where $ho, \varphi, z$ are cylindrical coordinates. (a) Write the Lagrangian for an unconstrained particle of mass...
Repeat the preceding problem for a particle sliding inside a smooth cone defined by $z=\alpha r$. Data from preceding problem A particle of mass $m$ slides inside a smooth paraboloid of...
Example 4.2 featured a bead sliding on a vertically-oriented helix of radius $R$. The angle $\theta$ about the symmetry axis was related to its vertical coordinate $z$ on the wire by...
What is the cost of capital and why is it important to a business? What are the different capital financing options available to organizations? What is working capital for short term business...
Use the following information on states of the economy and stock returns to calculate the standard deviation of returns. Assume that all three states are equally likely. (Do not round intermediate...
You are analyzing a stock. The stock's most recent dividend paid was $2.9 per share. You expect the stock dividends to grow at 20% for the next three years (until t = 3), followed by a long-term...

The restoring force of an anharmonic oscillator is proportional to the cube of the displacement. Show that

Question:

Step by Step Answer:

A force proportional to q3 implies a potential energy proportio...View the full answer

Statistical Mechanics

Students also viewed these Sciences questions