00:01
Okay, so for this question, we are trying to work out what is the equivalent spring constant of a single spring that behaves the same as this series combination of two springs.
00:12
So we're going to think about what happens if we apply a force down here.
00:17
So we're applying a force to this spring here.
00:21
So we know that the force will produce a deaf information equal to minus k2 times the extension of spring 2.
00:31
But this force is also transmitted.
00:33
So this force will be the same force that is acting on k1.
00:38
So it's still f, and it will produce a deformation given by this equation here.
00:45
So we can see from these equations that the deformation of the first spring is equal to minus f over k1, and the deformation of the second spring is equal to the same force, divided by the second spring constant.
01:06
Now thinking about what happens if we apply this to a single spring, it's the same force, and that force will give us a deformation depending on the equilibrium spring constant.
01:20
And for it to behave the same, that deformation must be equal to the sum of the two deformations we got from the original two springs.
01:28
So x1 plus x2 must give us this...