Particle motion of P consists of a periodic oscillation

In summary, the conversation discusses a particle P with mass m moving on the x-axis under a force field with potential energy V=V0(x/b)^4. It is shown that the motion of P is a periodic oscillation centered at the origin, with a period tau given by tau=2sqrt(2)*(m/V0)^0.5*(b^2/a)*integral of dvarsigma/(1-varsigma^4)^0.5, where the interval is 0<=x<=1. The problem mentions using the equation for motion, dx/dt=+-[2(E-V(x))]^0.5, but it is unclear how to use it to derive an equation for the oscillation amplitude.
  • #1
Benzoate
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Homework Statement



A particle P of mass m moves on the x-axis under the force field with potential energy V=V0(x/b)4, where V0 and b are positive constants. Show that any motion of P consists of a periodic oscillation with centre at the origin. Show further that, when oscillation has amplitude a, the period tau is given by

tau=2sqrt(2)*(m/V0)^(.5)*((b^2)/a)[tex]\int[/tex] d[tex]\varsigma[/tex]/(1-[tex]\varsigma[/tex]^4]).5), interval is : 0[tex]\leq[/tex]x[tex]\leq[/tex]1

Homework Equations


The Attempt at a Solution



Not really sure what equation I am supposed to derived.

since the problem mentions motion, I should probably start off with the equation for motion

dx/dt=+[2(E-V(x))].5

dx/dt=-[2(E-V(x))].5
 
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  • #2
Maybe I should rephrase the question : Anybody having trouble reading my OP?
 
Last edited:

1. What is particle motion of P?

Particle motion of P refers to the movement of a single particle, P, in a given space. This motion can be described in terms of its position, velocity, and acceleration over time.

2. What is periodic oscillation?

Periodic oscillation is a type of motion where the particle repeats its movement in a regular pattern or cycle. This means that the particle will return to its original position and velocity after a certain amount of time.

3. How is particle motion of P related to periodic oscillation?

Particle motion of P can exhibit periodic oscillation when the particle's motion follows a repeating pattern or cycle. This means that the particle's position, velocity, and acceleration will repeat themselves over time.

4. What factors affect the particle motion of P?

The particle motion of P can be affected by various factors such as the initial position and velocity of the particle, external forces acting on the particle, and the properties of the medium through which the particle is moving.

5. How can particle motion of P be represented graphically?

Particle motion of P can be represented graphically by plotting the position, velocity, or acceleration of the particle against time. This can help visualize the particle's movement and any patterns or cycles present in its motion.

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