Question: Consider a simple harmonic oscillator. Calculate the time averages of the kinetic and potential energies over one cycle, and show that these quantities are equal.

Consider a simple harmonic oscillator. Calculate the time averages of the kinetic and potential energies over one cycle, and show that these quantities are equal. Why is this a reasonable result? Next calculate the space averages of the kinetic and potential energies. Discuss the results.

Step by Step Solution

★★★★★

3.34 Rating (166 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a Time average The position and velocity for a simple harmonic oscillator are given by x A sin cot x ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

P-C-D-O (4).docx

120 KBs Word File

Students Have Also Explored These Related Classical Dynamics Of Particles Questions!

A simple harmonic oscillator takes 12.0 s to undergo five complete vibrations. Find (a) The period of its motion, (b) The frequency in hertz, and (c) The angular frequency in radians per second.

Is the acceleration of a simple harmonic oscillator ever zero? If so where?

Calculate the average value of the kinetic and potential energies for the H atom in its ground state.

watch the three short clips below then answer the questions Copy and paste the three links below 1) Projectile Motion https://www.nsf.govews/mmg/mmg_disp.jsp?med_id=72205&from= 2) Newton's Second Law...

c. What are the amplitude, period, and angular frequency wo of the H atom's oscillation? (A) = P3 - Pz = P2-P, = 0.01nm am! = A = 0. 0Inm angular Wo=zt T= LS- L, Wo= er Frequency = = 1. 16 x10-175...

Can you please identify the key themes of this assignment, because I am confused and don't know how to do that. thank you indeed. Question 1: The magnitude and direction of a vector are its two...

Provide a summary technical report with your own words about Pipelined Execution which is also named as Instruction Level Parallelism, addressing mainly the following areas: 1. What is Pipelined...

pls help. I'm struggling on using the solve_ivp (for a) and solve_bvp (for b and c) functions. please can you show me how to part a and b,c please? Question 12: Consider the one-dimensional,...

The excel homework assignment below has five tabs that cover five different topics: Net Present Value Analysis, Capital Budgeting and Cost of Capital, Working Capital, Management, Financial Ratio...

In a situation in which data are known to three significant digits, we write $6.379 \mathrm{m}=6.38 \mathrm{m}$ and $6.374 \mathrm{m}=6.37 \mathrm{m} .$ When a number ends in $5,$ we arbitrarily...

The Sports Equipment Division of Harrington Company is operated as a profit center. Sales for the division were budgeted for 2014 at $900,000. The only variable costs budgeted for the divisions were...

Why should questions on similar topics be clustered together?

16.38 Using the average baseball salary data for Problem 16.18 on page 602 and Problem 16.30 on page 612 (stored in MLB Salaries ), a. perform a residual analysis for each model. b. compute the...

The Global Oil Company (Global Oil) is an international producer, refiner, transporter and distributor of oil, gasoline and petrochemicals. Global Oil is a holding company with subsidiary operating...

Slagle Corporation is a large manufacturing organization. Over the past several years, it has obtained an important component used in its production process exclusively from Harrison, Inc., a...

Kalinda is currently studying architecture at Moonush University in Australia. Born in London, United Kingdom, Kalinda moved to Melbourne, Australia with her parents and brother when she was three...

Mr. Musk is issuing today 3 percent annual coupon bond for 1000. The bond has 10 years to maturity. You are a conservative investor, and believe that bonds are less risky than stocks, so you decide...

Assuming int numbers[SIZE];is initialized somehow, write a function counter() that you can send the array to, plus an extra integer, and the function will return the number of times that value is...

A 0.25-kg ball moving in the +x-direction at 13 m/s is hit by a bat. Its final velocity leaving the bat is 19 m/s in the x-direction. The bat acts on the ball for 0.010 s. Find the average force F...

Requirement 1. Use the EOQ model to determine the optimal number of pairs of shoes per order. Begin by selecting the formula used to calculate EOQ. ( D= Demand in units for one year, P= Ordering cost...

Two firms, No Leverage Inc. and High Leverage Inc. have equal levels of operating risk and differ only in their capital structure. No Leverage is unlevered and High Leverage has $ 5 0 0 , 0 0 0 of...

A bank has decided to set its interest rates to compound monthly on all deposits in order to give customers the same benefits as its current offering of 3.39% compounded quarterly. At what value...