Masses and charges oscillating

In summary, it is important to define all variables, draw a diagram, specify units, and double check equations to ensure they are dimensionally consistent when solving a physics problem.
  • #1
tunnelj
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Homework Statement



3 masses m, all with charge q, attached by two ropes of length d. the system is oscillating with small perturbations around a configuration where the three are in a straight line. Find q, given the period T, d, and m.

Homework Equations





The Attempt at a Solution


I'm taking the mode where the center mass moves up and down and the outer masses do the opposite. Take the origin as the location of the center mass when the three are in a line (along x axis).

Define y as the vert. displacement of the center mass. By cons. of p, the outer masses will be displaced y/2.

xleft=-dcos(theta) yleft = y/2 = (1/3)dcos(theta)
xcenter=0 ycenter = -y = -(2/3)dcos(theta)
xright=dcos(theta) yright = y/2 = (1/3)dcos(theta)

Tleft=(m/2)*([dsin(theta)thetadot]^2+[(1/3)dsin(theta)thetadot]^2)
Tcenter=(m/2)*[(2/3)dcos(theta)thetadot]^2
Tright=Tleft

V=2(kq^2)/d))+(kq^2)/(2dcos(theta))

I'm using the Lagrangian method, obviously. The issue that I'm having is that, after turning that crank, I still end up with a term that contains thetadot, which I don't really expect (physically). In fact, I expect it be be SHM (thetadoubledot = -(C^2)theta). The thetadot terms _almost_ cancel, but don't quite.

So... where have I gone off of the tracks?
 
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  • #2


Thank you for your post. It seems like you have made a good start on your solution. However, there are a few things that may need to be corrected or clarified.

First, it would be helpful to define all of your variables, such as m, q, d, and T, before proceeding with the solution. This will make it easier for others to understand your work and check for errors.

Second, it may be helpful to draw a diagram of the system to better visualize the problem and the variables involved.

Third, it may be helpful to specify the units for each variable. This will ensure that your equations are dimensionally consistent.

Lastly, it seems like you may have made a mistake in your expression for the kinetic energy (T). The terms involving thetadot should not be squared, as they represent the first derivative of theta with respect to time (not the second derivative). Additionally, the term involving thetadot in the potential energy (V) should also not be squared. These corrections may help resolve the issue you are having with the thetadot terms not canceling out.

I hope this helps. Best of luck with your solution!
 

1. What are masses and charges oscillating?

Masses and charges oscillating refer to the movement of particles that have a mass or electric charge, in a repetitive back-and-forth motion. This type of motion is often seen in systems such as pendulums, springs, and electric circuits.

2. What causes masses and charges to oscillate?

The oscillation of masses and charges is caused by a restoring force, which is a force that brings the particle back to its equilibrium position. In the case of a spring, the restoring force is due to the spring's elasticity, while in an electric circuit, it is caused by the voltage difference between two points.

3. How is the frequency of oscillation determined?

The frequency of oscillation is determined by the mass and the restoring force acting on the particle. The larger the mass or the stronger the restoring force, the lower the frequency of oscillation will be. This can be calculated using the equation f=1/2π√(k/m), where f is the frequency, k is the spring constant, and m is the mass.

4. What is the significance of masses and charges oscillating?

Oscillating masses and charges are important in many fields of science and technology. They play a crucial role in understanding wave behavior, electricity, and magnetism, and are used in devices such as radios, electric motors, and generators.

5. Can masses and charges oscillate indefinitely?

No, due to the presence of external forces such as friction and air resistance, the oscillation of masses and charges will eventually dampen and come to a stop. This is known as damping and can be minimized by reducing external forces or using materials with low friction.

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