# 2 Masses connected by a spring

• glover261
In summary, you have not provided any information about the variables in your problem, or how you are trying to solve it.
glover261
Hello I am trying to find the acceleration of a system that has 2 masses, m1 and m2 connected via a spring with a spring constant of k with a force of F applied to the larger mass in the direction that stretches the spring.

Very good. How are you going about it?
ie. did you try Newton's method of drawing free body diagrams for each mass?

Simon Bridge said:
Very good. How are you going about it?
ie. did you try Newton's method of drawing free body diagrams for each mass?

Yeah I found the forces acting downwards but I think they are irrelevant because all the acceleration for the system would be in the sideways direction. I found that the acceleration of the 3kg (larger) mass is 15/3= 5ms/^2, but I'm not sure if this is correct because wouldn't the spring be pulling back on it and therefore lowering its acceleration? I am not really sure how to find the acceleration of the whole system, do I try find the acceleration of each mass and add them? How do I do that when a spring is involved?

glover261 said:
Yeah I found the forces acting downwards but I think they are irrelevant because all the acceleration for the system would be in the sideways direction.
I think you may have left out some important information in your problem statement:
I was imagining both masses on a level frictionless surface with one to the left of the other ... in that situation the sum of the vertical (acting downwards) forces is zero.

I found that the acceleration of the 3kg (larger) mass is 15/3= 5ms/^2,...
This cannot follow from post #1 because you have not given any values for m1, m2 or F. It is unlikely to be correct because you have not accounted for the force from the spring.

...but I'm not sure if this is correct because wouldn't the spring be pulling back on it and therefore lowering its acceleration?
Yes.

I am not really sure how to find the acceleration of the whole system, do I try find the acceleration of each mass and add them?
This is not how you would normally treat the accelerations of coupled masses is it?

How do I do that when a spring is involved?
You include the force due to the spring in the free body diagram.
Think how you would do this problem if the spring were replaced by a string?

## 1. What is a "2 Masses connected by a spring" system?

A "2 Masses connected by a spring" system is a physical system consisting of two masses that are connected by a spring. The masses are usually denoted as m1 and m2, and the spring has a spring constant k. This system is commonly used in physics to study the behavior of oscillating systems.

## 2. What is the equation of motion for this system?

The equation of motion for a "2 Masses connected by a spring" system is given by:

m1x1'' + k(x1-x2) = 0

m2x2'' + k(x2-x1) = 0

where x1 and x2 are the displacements of m1 and m2, respectively, and the double prime represents the second derivative with respect to time.

## 3. What is the natural frequency of this system?

The natural frequency of a "2 Masses connected by a spring" system is given by:

ω = √(k/m)

where k is the spring constant and m is the reduced mass of the system, given by m = (m1m2)/(m1+m2).

## 4. How does the spring constant affect the motion of this system?

The spring constant, k, affects the motion of this system by determining the strength of the spring force. A higher spring constant will result in a stronger spring force, causing the masses to oscillate at a higher frequency and with smaller amplitudes. A lower spring constant will result in a weaker spring force, causing the masses to oscillate at a lower frequency and with larger amplitudes.

## 5. How do the masses affect the motion of this system?

The masses, m1 and m2, affect the motion of this system by determining the inertia of the system. A higher mass will result in a lower natural frequency and larger amplitudes of oscillation, while a lower mass will result in a higher natural frequency and smaller amplitudes of oscillation.

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