How does drag force affect the equations for masses attached by a spring?

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SUMMARY

The discussion centers on the dynamics of two masses connected by a spring, influenced by a drag force represented by F = -bv. The first equation derived is k(x2 - x1) - bv = ma1, where k is the spring constant, and x1 and x2 are the positions of the masses. The second equation, however, presents confusion regarding the sign of the drag force, leading to the equation -k(x2 - x1) + bv = ma2. The resolution lies in recognizing that the drag force should consistently be expressed as -bv, regardless of the direction of velocity, ensuring the equations remain valid for both masses.

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  • Understanding of Newton's laws of motion
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  • Basic proficiency in writing and solving differential equations
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uriwolln
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so let's say you have two masses attached by a spring in the middle. Also, there is a drag force proportional to the speed, that is F= -bv.

I have this problem of writing the equations right.
I envision, that I get the masses far apart, so I know there will be force exerted by the spring to the right, trying to return the the equilibrium position.
Thus, one equation will be
k(x2-x1) - bv = ma1
x1 and x2 represent the distance.
So here is my problem. For the second equation, its natural to think that by Newton's third law there will be an opposite force exerted by the spring, on the second mass, and so I assume the second mass wants to move to the left, because of that spring. The equation I get is:
-k(x2-x1) + bv =ma2.

This is the problem. In the second equation, in answers I am seeing, bv should be -bv, and I have no idea why! since I take moving right as positive, the second mass is moving left so it should turn positive.

PLZ, what am I missing?
 
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How exactly do you determine the coordinates x1 and x2 ?
Coordinate and acceleration carry the subscript 1 and 2. Why is it the velocity v doesn't carry subscript?
 
true, my mistake on this one...
but I think I've got my answer in a way. Because I do not know which direction the velocity goes to, I can not decide on the sign to give it, all I know the force opposes the movement, so I think I should always keep it on -bv, and the equations will work out if the velocity is positive or negative
 

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