# Pulleys and Springs: Really stupid question

So I am trying to follow along this example in the text to find keq of the system.

I can follow everything up until the point that they say: "It follows that x=2(x1+x2)

where:

x = displacement of mass
x1 =displacement of Pulley1cm
x2 =displacement of Pulley2cm

I am not seeing it. I am also very tired. So please help me and then slap me

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rl.bhat
Homework Helper
For the time being, suppose k2 is not operating. When the pulley1 moves up through x1, what is the distance moved by the mass ?

Yeah. I don't see it. How ca I relate anything to x?

Like rl.bhat says: If k2 was not operating, I know that 2W=k1*x1 ... but I
don't see how that helps?

Anyone?

rl.bhat
Homework Helper
Just compare the movement of the pulley and release of the rope at mass end.
When the pulley1 moves through x1, mass moves through y1 distance ,then y1 = 2x1. Similarly for pulley 2, y2 = 2x2. So the distance moved by the mass y1 + y2 = x = 2(x1 + x2)

Okay. I mean, I believe you. I just don't see it.

rl.bhat
Homework Helper
Okay. I mean, I believe you. I just don't see it.
When p1 moves up through x1, on both side of the pulley x1 rope is released. That adds up to 2x1.

When p1 moves up through x1, on both side of the pulley x1 rope is released. That adds up to 2x1.
Ahh. I think I see it now. Thanks for your patience!