Oscillations and inverse square law

In summary, the problem involves a particle of mass m moving in 1 dimension with two forces acting on it: a constant force towards the origin with magnitude B and an inverse square law repulsive force with magnitude A/x^2. The equilibrium position can be found by solving the equation m\ddot x=\frac{A}{x^2}-B sign(x) for both positive and negative values of x. Both Shyan and Anchit's attempts ignore important aspects of the problem and should be corrected.
  • #1
Anchit
1
0

Homework Statement



A particle of mass m moves in 1 dimension along positive x direction.It is acted on by a constant force directed towards origin with magnitude B,and an inverse square law repulsive force with magnitude A/x^2.Find equilibrium position.

Homework Equations



B+A/x^2=m*a

The Attempt at a Solution



B+A/x^2=0
x=sqrt(-A/B)

Is this correct?
 
Physics news on Phys.org
  • #2
No, the correct form is:
[itex]
m\ddot x=\frac{A}{x^2}-B sign(x)
[/itex]

Where [itex] sign(x)=\left\{ \begin{array}{ll} 1 & x>0 \\ 0 & x=0 \\ -1 & x<0 .\end{array} \right. [/itex]

Then you should solve for x<0 and x>0 separately. I hope the particle won't pass the origin!
 
  • #3
Shyan said:
No, the correct form is:
[itex]
m\ddot x=\frac{A}{x^2}-B sign(x)
[/itex]

Shyan's equation ignores the fact that the inverse square force also changes sign on opposite sides of the origin. If you include that fact, the sign() function can be simplified away.

Anchit's equation ignores the sign convention assumed in the problem: Both A and B are positive there. We do not want to be taking the square root of a negative number!

Heed Shyan's advice and look for both positive and negative solutions.
 

1. What is an oscillation and how does it relate to the inverse square law?

An oscillation refers to a repeating or back-and-forth motion. The inverse square law states that the intensity of a physical quantity, such as light or gravitational force, decreases in proportion to the square of the distance from the source. In other words, as the distance from the source doubles, the intensity decreases by a factor of four. Oscillations are often observed in systems that are governed by the inverse square law, such as a pendulum or a planet orbiting around a star.

2. What are some examples of oscillations that follow the inverse square law?

Some common examples of oscillations that follow the inverse square law include the motion of a pendulum, the oscillation of a spring, and the orbit of a planet around a star. Other examples include the intensity of light from a point source, the force between two electric charges, and the force between two masses due to gravity.

3. How does the inverse square law affect the amplitude of an oscillation?

The inverse square law does not have a direct effect on the amplitude of an oscillation. However, it does affect the intensity of the force or physical quantity that is causing the oscillation. This, in turn, can affect the amplitude of the oscillation. For example, in a spring-mass system, the amplitude of the oscillation will decrease as the distance between the spring and the mass increases due to the inverse square law.

4. Are there any exceptions to the inverse square law?

While the inverse square law is a fundamental principle in physics, there are some instances where it may not hold true. For example, at very small distances, such as in the case of subatomic particles, other forces may become more dominant and the inverse square law may not accurately describe the behavior of the system. Additionally, in certain scenarios, such as in a highly non-uniform medium, the inverse square law may not apply.

5. How is the inverse square law used in practical applications?

The inverse square law has many practical applications in fields such as physics, astronomy, and engineering. For example, it is used in designing satellite communication systems, calculating the intensity of light at different distances from a source, and determining the gravitational force between celestial bodies. The inverse square law is also used to understand and predict the behavior of many natural phenomena, such as the strength of earthquakes and the spread of diseases.

Similar threads

  • Introductory Physics Homework Help
Replies
8
Views
876
  • Introductory Physics Homework Help
Replies
13
Views
577
  • Introductory Physics Homework Help
Replies
10
Views
2K
  • Introductory Physics Homework Help
Replies
21
Views
607
Replies
8
Views
763
  • Introductory Physics Homework Help
Replies
31
Views
971
  • Introductory Physics Homework Help
Replies
11
Views
168
  • Introductory Physics Homework Help
Replies
3
Views
308
  • Introductory Physics Homework Help
Replies
4
Views
758
  • Introductory Physics Homework Help
Replies
17
Views
277
Back
Top