Natural oscillation period for elastic spring

In summary, the problem involves a linear elastic spring with spring constant E and a mass m attached to the right terminal. The tension is given by sigma = E*epsilon, where epsilon is the strain. The one dimensional equation of motion for elastic media is \frac{\partial^2 u}{\partial t^2} = (\frac{\lambda + 2\mu}{\rho})\frac{\partial^2 u}{\partial x^2} , and the relation between stress and strain is \sigma = E\frac{\partial u}{\partial x}. It is unclear which equations should be used for this problem.
  • #1
MaxManus
277
1

Homework Statement



I have a linear elastic spring with spring constant E, The spring is mass less, and is held fixed at the left terminal and has a mass m attached on the right terminal. We can neglict gravitational forces.

Find the natural oscillation when the tension sigma = E*epsilon, where epsilon is the strain.

The Attempt at a Solution



The one dimensional strain tensor is epsilon = du/dx
The one dimensional equation of motion for elastic media =
[tex] \frac{\partial^2 u}{\partial t^2} = (\frac{\lambda + 2\mu}{\rho})\frac{\partial^2 u}{\partial x^2} [/tex], am I supposed to use this equation?

[tex] \sigma = E\epsilon[/tex]
[tex] \sigma = E\frac{\partial u}{\partial x} [/tex]

Homework Statement


Homework Equations


The Attempt at a Solution

 
Last edited:
Physics news on Phys.org
  • #2
Anyone? I don't know which equations I should use so any help would help. F.ex this is a transverse wave?
 

What is a natural oscillation period for an elastic spring?

A natural oscillation period for an elastic spring is the time it takes for the spring to complete one full cycle of oscillation, starting from its initial position and returning back to that same position. It is determined by the physical properties of the spring, such as its mass and stiffness, and is independent of any external forces or factors.

How is the natural oscillation period of an elastic spring calculated?

The natural oscillation period of an elastic spring can be calculated using the equation T = 2π√(m/k), where T represents the period in seconds, m is the mass of the spring in kilograms, and k is the spring constant in Newtons per meter.

What factors can affect the natural oscillation period of an elastic spring?

The natural oscillation period of an elastic spring can be affected by changes in its physical properties, such as its mass or stiffness. Additionally, external factors such as temperature, air resistance, and gravity can also impact the spring's oscillation period.

Can the natural oscillation period of an elastic spring be changed?

Yes, the natural oscillation period of an elastic spring can be changed by altering its physical properties or by applying external forces. For example, increasing the spring's stiffness will result in a shorter oscillation period, while adding weight to the spring will increase its oscillation period.

What is the significance of the natural oscillation period for an elastic spring?

The natural oscillation period for an elastic spring is an important factor to consider in various scientific and engineering applications. It can help determine the stability and performance of structures that use springs, such as bridges or buildings, and is also used in the design of various mechanical systems, such as shock absorbers and pendulums.

Similar threads

  • Advanced Physics Homework Help
Replies
11
Views
2K
  • Advanced Physics Homework Help
Replies
3
Views
4K
  • Advanced Physics Homework Help
Replies
7
Views
2K
  • Advanced Physics Homework Help
Replies
3
Views
2K
  • Advanced Physics Homework Help
Replies
5
Views
1K
  • Advanced Physics Homework Help
Replies
3
Views
5K
  • Advanced Physics Homework Help
Replies
1
Views
2K
  • Advanced Physics Homework Help
Replies
5
Views
2K
  • Advanced Physics Homework Help
Replies
1
Views
1K
  • Calculus and Beyond Homework Help
Replies
5
Views
559
Back
Top