Electrical Forces in Simple Harmonic Motion: Finding Frequency and Amplitude

  • Thread starter Thread starter duke13
  • Start date Start date
  • Tags Tags
    Electrical Forces
AI Thread Summary
The discussion centers on a physics problem involving a point mass with charge q moving vertically in a frictionless cylinder, influenced by another charge Q at the bottom. The charge q is released from height H and comes to rest at height h above Q, where it begins to oscillate. The key point is demonstrating that the motion will be simple harmonic if the condition H - kqQ/(mgH) is significantly less than the square root of (kqQ)/(mg). The derived height h is kqQ/(Hmg), and it is confirmed that simple harmonic motion (SHM) occurs when the net force acting on the charge is proportional to its displacement from the equilibrium position, akin to Hooke's Law. The frequency of the oscillation is calculated to be 4 times the cube root of (mg^3)/(4π^4kqQ).
duke13
Messages
1
Reaction score
0
can anyone help with this?
a small point mass m carries a charge q. it is constrained to move vertically inside a narrow, frictionless cylinder. at the bottom of the cylinder is another point mass of Charge Q, same sign as q. the charge q is released from a height H and is observed to fall vertically downwards until it comes to rest for the first time at a vertical height h above Q. the charge then oscillates vertically. show that the motion will be simple harmonic if H-kqQ/(mgH) is much less than ((kqQ)/(mg))^.5. and the frequency will equal 4((mg^3)/(4pi^4kqQ)).



thanks, have been able to show h = kqQ/(Hmg)
 
Physics news on Phys.org
SHM will occur if the net force that pulls an object toward an equilibrium position is directly proportional to the displacement from that equilibrium position (such as Hooke's Law, F=-kx).
DOes your equation satisfy this requirement?
 

Thread 'Maxwell stress tensor'

This is from Griffiths' Electrodynamics, 3rd edition, page 352. I am trying to calculate the divergence of the Maxwell stress tensor. The tensor is given as ##T_{ij} =\epsilon_0 (E_iE_j-\frac 1 2 \delta_{ij} E^2)+\frac 1 {\mu_0}(B_iB_j-\frac 1 2 \delta_{ij} B^2)##. To make things easier, I just want to focus on the part with the electrical field, i.e. I want to find the divergence of ##E_{ij}=E_iE_j-\frac 1 2 \delta_{ij}E^2##. In matrix form, this tensor should look like this...
View full post »
Thread 'Applying the Gauss (1835) formula for force between 2 parallel DC currents'

Thread 'Applying the Gauss (1835) formula for force between 2 parallel DC currents'

Please can anyone either:- (1) point me to a derivation of the perpendicular force (Fy) between two very long parallel wires carrying steady currents utilising the formula of Gauss for the force F along the line r between 2 charges? Or alternatively (2) point out where I have gone wrong in my method? I am having problems with calculating the direction and magnitude of the force as expected from modern (Biot-Savart-Maxwell-Lorentz) formula. Here is my method and results so far:- This...
View full post »

Similar threads

Harmonic Motion of a Charged Particle
Replies
1
Views
3K
Electric potential energy between charge and moving magnet
Replies
7
Views
2K
B Ion Trap and Time-Varying Potentials
Replies
1
Views
1K
Falling charged objects paradox?
Replies
11
Views
2K
Find net velocity of charged particle in electric field (symbols only)
Replies
14
Views
3K
When Do Sand Particles Slip Off a Vibrating Plate?
Replies
13
Views
1K
Initial velocity of bird landing on horizontal wire modeled as spring
Replies
7
Views
974
Position and acceleration in simple harmonic motion given velocity
Replies
16
Views
1K
EMF due to Lorentz electric and magnetic forces
Replies
3
Views
1K
Frequency of Undamped Driven Oscillator near Zero
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top