Finding the Period of a Mass Connected to Two Springs in Series

In summary, the conversation discusses a problem involving a mass connected to two springs with different spring constants. The first setup has the springs connected in series and the mass resting on the floor. The goal is to find the period for this configuration, which is given by T=2\pi\sqrt{m(\frac{1}{k_{1}}+\frac{1}{k_{2}})}. The approach discussed involves replacing the two spring system with a single spring and using the fact that the magnitude of force at each junction is the same. This assumption is possible because the springs are massless.
  • #1
Opus_723
178
3

Homework Statement



EDIT: I have removed the second setup, since I solved it. I still can't figure out this one though.

A mass m is connected to two springs, with spring constants k[itex]_{1}[/itex] and k[itex]_{2}[/itex].

The first setup has both springs connected in series, connecting the mass horizontally to the wall, with the mass resting on the floor. Show that the period for this configuration is given by

T=2[itex]\pi[/itex][itex]\sqrt{m(\frac{1}{k_{1}}+\frac{1}{k_{2}})}[/itex]

Hopefully I described the diagram sufficiently.

The Attempt at a Solution



Not really sure where to start. My first thought was to try and come up with an equation of motion, but honestly we haven't learned differential equations yet, so I don't think that's how I'm supposed to do it. Anyway, I can't seem to get it in terms of x regardless, since each spring presumably stretches a different length. I know that the two lengths will add up to the total displacement of the mass, but that only let's me get rid of one variable. So finding an equation of motion doesn't seem to be working for me. And even if I found it, I don't know how much good it would do me unless it turned out to be a real easy differential equation.

Anyway, this is all I got:

F = -k[itex]_{1}[/itex]x[itex]_{1}[/itex]-k[itex]_{2}[/itex]x[itex]_{2}[/itex]

x[itex]_{1}[/itex]+x[itex]_{2}[/itex] = x
 
Last edited:
Physics news on Phys.org
  • #2
One way of approaching the problem is to ask yourself, if I was to replace the two spring system with a single spring (for which I know how to obtain the period), what should be the spring constant of the single spring?

Hint: The magnitude of force at each junction (wall-spring1, spring1-spring2, spring2-mass) is the same.
 
  • #3
Well, if I assume the force is the same at each junction, that makes the problem much easier. But how do we know that? Is it because the springs are massless, so the force at one end has to be the same as the force at the other?
 
  • #4
Yes.
 
  • #5
Great. That clears it up. Thanks a lot!
 

1. What is a mass connected to two springs system?

A mass connected to two springs system is a simple mechanical system where a mass is attached to two springs, allowing it to oscillate back and forth between the two springs.

2. What is the equation for calculating the period of a mass connected to two springs system?

The equation for calculating the period of a mass connected to two springs system is T = 2π√(m/k), where T is the period, m is the mass, and k is the spring constant.

3. How does changing the mass affect the period of a mass connected to two springs system?

Changing the mass in a mass connected to two springs system will affect the period by directly proportional relationship. As the mass increases, the period will increase and vice versa.

4. What happens to the period when the spring constant is doubled in a mass connected to two springs system?

In a mass connected to two springs system, when the spring constant is doubled, the period will be reduced by a factor of √2. This means that the mass will oscillate faster between the two springs.

5. Can the mass connected to two springs system exhibit simple harmonic motion?

Yes, the mass connected to two springs system can exhibit simple harmonic motion as long as the force exerted by the springs is directly proportional to the displacement of the mass from its equilibrium position.

Similar threads

  • Introductory Physics Homework Help
2
Replies
56
Views
2K
  • Introductory Physics Homework Help
Replies
24
Views
890
  • Introductory Physics Homework Help
Replies
3
Views
183
  • Introductory Physics Homework Help
Replies
8
Views
274
  • Introductory Physics Homework Help
Replies
10
Views
754
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
17
Views
236
  • Introductory Physics Homework Help
Replies
22
Views
442
  • Introductory Physics Homework Help
Replies
29
Views
822
  • Introductory Physics Homework Help
Replies
2
Views
2K
Back
Top