HomeworkLib
Question

1) Consider a one dimensional potential given by U (x )=ax 8−bx6 . a) What are...

1) Consider a one dimensional potential given by U (x )=ax 8−bx6 . a) What are the units of the constants a and b? b) For positive values of s a and b, find the equilibrium points for this potential and determine if they are stable or not. c) What is the frequency of small oscillations about the stable equilibrium points?

science   physics   
0 0
Add a comment Improve this question Transcribed image text
Next > < Previous
Sort answers by oldest

Homework Answers

Answer #1

Dear student,
Find this solution.if any issue with that don't forget to write in comment section.I will rectify them as soon as possible.
If you find the solution helpful and kindly RATE THE ANSWER it would be appreciated.
Your rating is important to me.
Thanks for asking..Jeule) neler) Soule っχ 千a SV 2 esuili brium 千a 2 う>。 2 clarly.atx- ь unstable

0 0
Add a comment
Know the answer?
Add Answer to:
1) Consider a one dimensional potential given by U (x )=ax 8−bx6 . a) What are...
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for? Ask your own homework help question. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions

  • The Lennard-Jones potential energy Ulj(x) is important in chemical bonding theory and is given by 1012...

    The Lennard-Jones potential energy Ulj(x) is important in chemical bonding theory and is given by 1012 ool ULJ 1 1 1 ULJ = 4€ | (x12 26 I 0 E 012 where e and o are constants and ř=r/o. (a) Sketch a graph of this potential energy. (b) Use IDL to obtain a careful graph of ULJ(x)/€ versus x/0. (c) Locate any equilibrium points, (d) determine which ones are stable, and (e) find the frequency of small oscillations about about...

  • A potential energy function is given by U(x) = (x ^−8) *e^ (x ^2) . Let’s...

    A potential energy function is given by U(x) = (x ^−8) *e^ (x ^2) . Let’s only focus on the region where x > 0. a) Find the position where the potential energy is a minimum b) For small oscillations around this minimum, what is the angular frequency ω? c) At what distance (either to the left or right) from the equilibrium point is the exact value of the force (derived from the full potential) more than 10% different from...

  • Consider a particle with a mass m subject to a force F(x) = ax - bx3...

    Consider a particle with a mass m subject to a force F(x) = ax - bx3 where x is the displacement of the origin of the reference system and a and b are positive constants. a) Find an expression of the particle's total energy. Show that this total energy is constant. b) Find the equilibrium points and determine if they are stable or unstable.

  • A potential-energy function in two dimensions is given by U(x)=a(x2−y2), where x and y measure position...

    A potential-energy function in two dimensions is given by U(x)=a(x2−y2), where x and y measure position in m and a is a positive constant with the units of J/m2J/m2. (a) Show that this function has an equilibrium at x=0, y=0. (b) Is the equilibrium stable against small displacements in the x-direction? What about the y-direction?

  • 5. One-Dimensional Potential Energy (20 points) A particle of mass m oscillates in a potential well...

    5. One-Dimensional Potential Energy (20 points) A particle of mass m oscillates in a potential well created by a one-dimensional force where a and b are known positive constants. Assume the particle is trapped in the well on the positive side of the y-axis. a) Find and expression for the potential energy U(x) for this force. (10 points) NOTE: There will be one undetermined constant. b) Set Umin, the minimum value for this potential energy function, equal to zero. Solve...

  • A particle is introduced to a region with a potential described by U(x)--2x2 +x*+1 Joules. 3. a. ...

    A particle is introduced to a region with a potential described by U(x)--2x2 +x*+1 Joules. 3. a. (2 pts) In software, plot the potential U) Set your axis ranges: -2 SxS2 and 0s b. (5 pts) Find the equilibrium positions and determine whether they are stable or c. (8 pts) Describe the motion of the particle for total energy values E-О.0.05. 1.0, 2.0 unstable. Explain how you arrived at your answers. (all in Joules). What I am looking for here...

  • Q) A one-dimensional potential is given by the formula U(x)=9(x-8)2 J, where x is in meters....

    Q) A one-dimensional potential is given by the formula U(x)=9(x-8)2 J, where x is in meters. If a mass of 2kg is placed at rest at the origin, what is the highest speed it will reach in its subsequent motion? ____m/s PLEASE EXPLAIN HOW THIS WAS SOLVED, THANK YOU!! Q2) Two identical blocks of mass 4kg are on a frictionless surface, one stationary, and the other moves towards it at a speed of 6m/s. Afterwards, the previously moving block moves...

  • Consider a one-dimensional well with one impenetrable wall. The potential energy is given by 0 x...

    Consider a one-dimensional well with one impenetrable wall. The potential energy is given by 0 x < 0 V(x) = { -V. 0 < x < a 10 x > a We showed in the homework that the allowed energies for the eigenstates of a bound particle (E < 0) in this potential well satisfy the transcendental function -cotĚ = 16 - 52 $2 where 5 = koa, and ko = V2m(Vo + E)/ħ, and 5o = av2mV /ħ (a)...

  • Q1) A one-dimensional conservative potential is given by U(x)=7x2J, with x measured in meters. If a...

    Q1) A one-dimensional conservative potential is given by U(x)=7x2J, with x measured in meters. If a 4kg particle starts at x=1 with a velocity of +10m/s, how fast will it be going when it reaches x=2 meters? please explain how you solved for this. Q2) A hand grenade has a mass of 6kg and it explodes into three pieces each of the same mass. Two of them go off, each with a speed of 17m/s with an angle of 60°...

  • A particle of mass 5 kg is subject to a conservative force whose potential energy (in...

    A particle of mass 5 kg is subject to a conservative force whose potential energy (in joules) as a function of position (in meters) is given by the equation U(x) =-100x5e-1x [where x > 0] (a) Determine the position xo where the particle experiences stable equilibrium (b) Find the potential energy Uo of the particle at the position x 2106 The particle is displaced slightly from position x = xo and released (c) Determine the effective value of the spring...

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT