1. Oscillations - Model Springs

How do I express each force of teh following spring in vector form and show that the position of the block is l0-(mg/2k)sin(alpha))

2. can some one please check I have this right?

each force in vector form is (N=normal force), W= Weight, H = spring force):

N=¦N¦.j

W=(W.i).i + (w.j).j = - ¦W¦sin(alpha)i + ¦W¦cos(alpha)j

H=-k(l-l0)s = -2k(x-l0)i (by hookes law)

To get the equilibrium I just made N+W+H = 0 and collected terms in i. I also replaced W by mg to get the equilibrium condition as shown

3. Originally Posted by moolimanj
can some one please check I have this right?

each force in vector form is (N=normal force), W= Weight, H = spring force):

N=¦N¦.j

W=(W.i).i + (w.j).j = - ¦W¦sin(alpha)i + ¦W¦cos(alpha)j

H=-k(l-l0)s = -2k(x-l0)i (by hookes law)

To get the equilibrium I just made N+W+H = 0 and collected terms in i. I also replaced W by mg to get the equilibrium condition as shown
That works, but make a distinction here:
H=-k(l-l0)s = -2k(x-l0)i
The k in the second term is not the same as the k in the last term, but you are using the same variable for it. Try
H=-K(l-l0)s = -2k(x-l0)i
or something.

-Dan