# Mass-Spring free body diagram

• dondiego
In summary, the equations for the first and second masses are: k(y1+d1) + k(y2-y1+d2) = my'' and k(y2-y1+d1) + k(y2+d2) = my''.

#### dondiego

I am trying to get started on a problem. I have two masses M1 = M2 and three springs all with the same constant. The weights and springs are on a frictionless table and the outer springs are attached to walls

Wall ~~~Mass~~~Mass~~~Wall

How do I draw the free-body diagram? I am confused about the forces. I know each mass has a spring force pulling it towards the wall and the middle spring should be a force on each mass in the opposite direction that the wall spring force is. Are these the only forces? Or do I need to show both wall spring forces on each mass?

Each mass connects to two springs and thus has two spring forces acting on it.

Yeah for each mass two spring forces are acting on it...thats all...
so for equilibrium and same spring constants and masses ... alll 3 springs will show same extension/deflection...

R Power said:
Yeah for each mass two spring forces are acting on it...thats all...
so for equilibrium and same spring constants and masses ... alll 3 springs will show same extension/deflection...

So I need to find the horizontal displacements Y1 and Y2 with Y1 the displacement on the first mass in the right direction and Y2 the displacement on the 2nd mass in the right direction.

The motion is started from rest with Y(0) = [1 1] and Y'(0) = [0 0]

Y(0) and Y'(0) should be vertical vectors, i.e one column but I did not know how to represent them that way.

I am also given that M=3kg and K=9N/m

I just want help in setting it up. I am coming up with these two equations but I don't know if it is right:

For the first mass -k(y1 +d1) + k(y2-y1+d2) = my''
For the 2nd mass -k(y2-y1+d1) + k(y2+d2) = my''

I'm not sure whether I should have the d terms in there or not (d is displacement) since they are starting at rest.

Last edited:
the d terms need not be there i think...then the equations seem correct.
Yeah! no d terms I'm pretty sure!

Reason: (y2 - y1) itself is the deflection of the second spring (starting from left) and y1 is the displacement of the first spring. So there is no way these extra d1 and d2 come from.

Actually I mean- d2= y2 - y1
d1= y1

Last edited:
R Power said:
the d terms need not be there i think...then the equations seem correct.
Yeah! no d terms I'm pretty sure!

Reason: (y2 - y1) itself is the deflection of the second spring (starting from left) and y1 is the displacement of the first spring. So there is no way these extra d1 and d2 come from.

Actually I mean- d2= y2 - y1
d1= y1

Thanks. I'm still working on it but that helps. I'm a 50 something engineering masters student and this stuff is not coming back to me very easy as it's been a long time since I got my BS. Of course back then, resources like this weren't here either!

Thanks!

## 1. What is a mass-spring free body diagram?

A mass-spring free body diagram is a visual representation of the forces acting on a mass-spring system. It includes the mass, spring, and any external forces acting on the system.

## 2. How do I draw a mass-spring free body diagram?

To draw a mass-spring free body diagram, you first need to identify all the forces acting on the system. This includes the weight of the mass, the tension in the spring, and any external forces. Then, draw a point to represent the mass and use arrows to represent the direction and magnitude of each force.

## 3. What is the purpose of a mass-spring free body diagram?

The purpose of a mass-spring free body diagram is to visually understand the forces involved in a mass-spring system. It helps to identify the equations that govern the motion of the system and can be used to solve for unknown variables.

## 4. What are the key components of a mass-spring free body diagram?

The key components of a mass-spring free body diagram are the mass, spring, and any external forces. The mass is represented by a point and the spring is represented by a line. The direction and magnitude of the forces are represented by arrows.

## 5. How does a mass-spring free body diagram relate to Newton's laws of motion?

A mass-spring free body diagram relates to Newton's laws of motion by illustrating the forces acting on a system and how they affect the motion of the mass. It helps to apply Newton's second law, which states that the net force on an object is equal to its mass multiplied by its acceleration.