Question

Newtons Second Law Question!

Answer 1

Super fun^(999)

Answer 2

F = m a = m (d/dt)dx/dt = - kx -b dx/dt

m (d/dt)dx/dt + kx + b dx/dt = 0 2nd order ODE

solutions

x = A exp(-bt/2m) cos(w' t + delta)

w' = sqrt (k/m - (b/2m)^2 )

I doubt you were expected to derive this, however. Good luck with evaluation.

Answer 3

where's the L factor in? Hmmmm

Answer 4

Yes, L comes in as the length of the unchanged spring,
so you have F = - k(x-L) which = 0 when x=L. Redefine x in the equations I gave you as x' = (x-L), displacement from equlibrium L. "F = -kx" was a bit misleading as it really has to be F proportional to displacement from L.

Answer 5

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Answer 6

@zepdrix so it's 10:25 PM and I'm terrified.

Answer 7

Sorry I have too much homework tonight :c I gotta get to work!

Answer 8

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Answer 9

@douglaswinslowcooper please help with writing out the problem, as I am having much difficulty.

Answer 10

What do you have so far? Can you work with x' = (x-L) and substitute it into what I wrote toward the beginning of this?

Answer 11

F = m a = m (d/dt)(x-L) = - kx -b (x-L)

Answer 12

m (d/dt)(x-L)+ kx + b (x-L) = 0

Answer 13

I have never taken physics so the question is quite confusing

Answer 14

Just replace x in my earliest answer with x' = (x-L) and put the equations in terms of x', including the answer

x' = x-L = A exp etc.

Then x = L + A exp etc.

Answer 15

This is for math course, not physics?

Answer 16

yes this is for differential equations

Answer 17

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Answer 18

I cannot draw, unfortunately.

Let's go to the questions as posed.

Create 2nd-order o.d.e. we have it: (d/dt)(dx'/dt) +b dx'/t + k x = 0


find the general solution. We have it x' = x-L etc or x = L+ etc.: Get the coefficientns from the values given for m, L, k, b.

Find the specific solution, when at t=0 x'(=x-L) = (5-7)=-2, dx'/dt = 1 cm/sec

Answer 19

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Answer 20

what does + etc mean?

Answer 21

That is neat. The solutions I gave above were for x = etc. and w' = etc. It seems as though one could plug the values from your question and get the answers they are seeking. It has been a long time since I have solved one of these in detail, which is why I had to look up the answer. What is missing in x=etc and w=etc ?

Answer 22

@mathmale please help

Answer 23

etc. means the rest of the equation I gave for x and for w far above at the beginning of this thread.

Answer 24

I'm sorry but none of this makes sense to me. Don't 2nd O.D.E have '' two '' of these '