Mass and springs problem

In summary, the frequency of oscillation of a block attached to two springs with spring constants k1=280 N/m and k2=260 N/m and mass m=14 kg is given by the equation frequency = square root of (3k/m), where k is the combined spring constant of the two springs. The forces on the block from the springs can be calculated by taking into account the displacement of each spring.
  • #1
smb62
4
0
suppose that the two springs have different spring constants k1=280 N/m and k2=260 N/m and the mass of the object is m=14 kg. Find the frequency of oscillation of the block in Hz.

http://www.physics.umd.edu/rgroups/ripe/perg/abp/think/oscil/mos.htm
the first picture on this site is what the problem looks like. Its a mass between two springs that are attached to walls.

i know that angular frequency equals the square root of k/m. but i don't know how to do it when there are two springs involved. Please help Asap. Thanks so much
 
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  • #2
Welcome to PF!
Let your origin be at where both springs has their rest length.
If you displace the box a distance "x", what are the forces (with direction) acting on it from either box?
 
  • #3
arildno said:
Welcome to PF!
Let your origin be at where both springs has their rest length.
If you displace the box a distance "x", what are the forces (with direction) acting on it from either box?

So if i have F1= -kx = -280x and F2= 260x do i then add them ? if so i would get Ft= -20x ...then should i use -20 as my value for k? and substitute it into the equation that i said before...where frequency equals the square root of (k divided by m)?

THanks so much for your help by the way...this forum is a wonderful idea and i am definitely going to spread the word!
 
  • #4
No that is incorrect!
Let the rest lengths be [tex]L_{1},L_{2}[/tex]
For clarity, "x" be a positive number.
Then, the new length of spring 1 is [tex]L_{1}+x[/tex]
Hence, [tex]F_{1}=-k(L_{1}+x-L_{1})=-kx[/tex]
Let's look at spring 2:
If spring 2 had been lengthened by a positive amount "y" (dragged out to the left), then, the force from it would drag the block to the right (the positive direction).
Hence, for positive displacement of spring 2 "y", [tex]F_{2}=2ky[/tex]
Now, setting y=-x (spring 2 is actually shortened), we get:
[tex]F_{2}=-2kx[/tex]

Hence, total force F on block is:
[tex]F=F_{1}+F_{2}=-3kx[/tex]
 

1. What is a mass and springs problem?

A mass and springs problem is a type of physics problem that involves the motion of a mass attached to one or more springs. It is commonly used to study simple harmonic motion and oscillations.

2. How do you solve a mass and springs problem?

To solve a mass and springs problem, you need to use the equation F = -kx, where F is the force exerted by the spring, k is the spring constant, and x is the displacement of the mass from its equilibrium position. You also need to apply the principles of conservation of energy and conservation of momentum.

3. What is the difference between a mass and springs problem and a simple harmonic motion problem?

A mass and springs problem is a specific type of simple harmonic motion problem that involves a mass attached to a spring. In other words, the mass and springs problem is a real-world application of simple harmonic motion.

4. Can a mass and springs problem be solved analytically?

Yes, a mass and springs problem can be solved analytically using mathematical equations and principles. However, in some cases, numerical methods may be needed to find a solution.

5. What are some real-world applications of a mass and springs problem?

Mass and springs problems have many real-world applications, such as studying the motion of a mass attached to a spring in a car's suspension system, analyzing the movement of a pendulum, or investigating the vibrations of a guitar string.

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