# Pendulum and spring

## Homework Statement

I have to derive equation of motion for this system. I want to use a moment of force, but i have a problem with moment of force spring.

## The Attempt at a Solution

What i've done is:
M(Fg)=-mgLsinα
M(N)=0
M(Fb)=mω^2 Lsinα*Lcosα
mL^2*α''=ΣM
M(Fs)=?

#### Attachments

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BvU
Homework Helper
You still haven't provided the full problem statement.
Nor any equations.
Are you supposed to do this classically, or with a Lagrangian ?
And, as I stated, ##F= - kx## is usual for a spring.

Did you read through the guidelines ?

So, i have to find equation of motion for this system. We know length of the line (L) and L1(picture). Initially the angle between spring and line(L) is 90, so initial length of the spring is √(L1^2-L^2). What's more the the pendulum rotates around the main rod (
angular velocity ω).
Yes my post was deleted.

BvU
Homework Helper
That all you have to describe the system (the full problem statement) ?
If so, are you allowed to make a small-angle approximation (##x = x_0 + L(\theta-\theta_0)## ) ?
If not, you have some trig to work out.
Are you supposed to do this classically, or with a Lagrangian ?

I'm supposed to this classically, but i'm not allowed to make a small-angle approximation. There is also dissipation F=-cl'. I can't even imagine how this system works. I worked out length of the spring (dependent on angle) using law of cosines, but i don't know if it's a good idea.

Last edited:
BvU
Homework Helper
Pretty awkward indeed. Don't know how to make it simpler, I'm afraid ... Apparently the full problem statement is still more involved ? Although -cL' is a constant (?)

No -cl' isn't constatnt, l(small L) is the length of the spring(dependent on the angle)

BvU
Homework Helper
That's not dissipation ! That's the spring (what I called ##
F= - kx ## ). Very nifty to use l' and L' for different quantities . Confusion assured !

The whole thing looks a bit like a steam engine governor with an extra spring: ##\omega## pushes the weight outward, gravity + spring pull it back.

initial length of the spring is √(L1^2-L^2).

And if it doesn't say what the equilibrium length is, you're stuck ! (unless your problem statement says somehow that it is zero).
You still haven't provided the full problem statement

In my exercise is:
Assume forces:
1. Spring elasticity: F=-kΔl
2. Dissipation/damping: F=-cl'
So I don't think it's the same.

TSny
Homework Helper
Gold Member
So l' is rate of change of l?

I still don't see a complete statement of the problem.

Yes l' is a derivative. It is all I have in my assignment