Time Period SHM of Two Springs with +Q & -Q Charges

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SUMMARY

The discussion focuses on calculating the Time Period of Simple Harmonic Motion (SHM) for two springs with charges +Q and -Q positioned at their ends. The relevant equations include the electrostatic force, F(elec) = (k Q^2) / (d^2), and the spring force, F(Spring) = (Kl). The confusion arises regarding the interaction between the electrostatic forces and the spring forces, particularly whether the spring force can counteract the electrostatic attraction before the charges collide. A detailed analysis involving differential equations may be necessary to fully understand the dynamics of the system.

PREREQUISITES
  • Understanding of electrostatics, specifically Coulomb's Law
  • Knowledge of Hooke's Law and spring constants
  • Familiarity with Simple Harmonic Motion principles
  • Basic differential equations for dynamic systems
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  • Learn about the interaction of electric and elastic forces in oscillatory motion
  • Explore differential equations related to coupled oscillators
  • Investigate the effects of varying spring constants on oscillation frequency
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Students and educators in physics, particularly those focusing on mechanics and electrostatics, as well as anyone interested in the dynamics of oscillatory systems involving multiple forces.

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Homework Statement



Two Springs are present (one just infront of the other). The Spring towards the left has +Q charge and towards the right -Q charge (at their ends).The distance between the two charges is d. The Springs are of length l. Find the Time Period of the Simple Harmonic Motion if the charges are of same mass. ( l > d )

Diagram
(Wall)-->(Spring)-->+Q -Q<--(Spring)<--(Wall)

Homework Equations



F(elec)=(k Q^2) / (d^2) where k=(1/4)∏ε
F(Spring)=( Kl )

The Attempt at a Solution



I know the above two equations, but can't proceed. Is there any other force too? I can't figure out why will the charges move back again? I'm having two confusions

1) The charges are opposite so they will attract each other. When they reach a certain point they will collide (as l > d ) and move back. Is this the reason why they move back? What other equation do i have to use?

2) Is it the Spring force will pulls the charges back before they collide. But it shouldn't be true as ( l > d ) and electrostatic forces are very strong and spring force cannot overcome it. Am i right? so how should i proceed

Pls help me...
 
Last edited:
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Hello there,
It would be of tremendous use, if you could provide us with a diagram of how the setup looks like, as it is rather unclear from the initial description.
Meaning,
Are the charges connected like so:
Q->spring->spring-(-)Q?
With the total distance d?
Or,
Fixture->Spring->Q-Spring-(-Q)->Fixture.
Are there any other limitations, constraints?
Beware that after you provide the full delineation of the problem, there might arise a need to solve a differential equation, so that you incorporate, simultaneously, the electric and elastic force.
Daniel
 

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