# Equation of motion for system of springs- SHM

## Homework Statement

I don't want to write the whole question as it is very long and I just have one query.. Basically the question involves a particle attached to three different springs which have fixed end points. In the question the mass of the particle is m, and the other constants used throughout are k (stiffness of one of the springs), g, and l0 which is the natural length of one of the springs. All the lengths in the question are given in terms of l0.
My question is this- my answer for the equation of motion doesn't contain the constant l0 in the part that determines the amplitude, only g, m and k. I've checked over and over and I can't find a mistake but to me this seems impossible. The answer I have includes l0 as the 'starting point' but the term involving cos does not depend on the length. Does this definetely mean I've made a mistake?

## Homework Equations

Hooke's Law, method for solving linear differential eq.

## The Attempt at a Solution

see above.

Related Calculus and Beyond Homework Help News on Phys.org
rock.freak667
Homework Helper
Do you have a diagram associated with it? That would help much in visualizing your problem.

Here you go..
To clarify my actual question, looking at the system below, (for the case where the mass starts from rest at x = 8/7l0) is it possible for the amplitude of the motion to not be dependant on l0.

#### Attachments

• 15 KB Views: 339
Last edited:
rock.freak667
Homework Helper
How did you derive your equation of motion, can you show your steps?

I'll write it out tomorrow if necessary as I need to go to bed now. But I'd really rather a 'yes/no' answer to my question- its a theoretical point. If it does definetely mean there is a mistake (as I think it does) then I have to really find it myself cos this is coursework. I just don't want to waste lots of time looking for a mistake that isn't there...

rock.freak667
Homework Helper
Your spring constants aren't the same, and the masses attached to springs A and B aren't the same, so I am to say that you have a system with 3 degrees of freedom?

The spring constants are different yes, but theres only one mass (m) in the system (ie so I've been looking simply at the forces acting on the 'particle' with mass m.)
Afraid I've never used the term 'degrees of freedom' so don't know what that implies..

rock.freak667
Homework Helper
Well in my experience with questions with such springs, none of the equations of motion I've derived contains the the natural length of the spring.

vela
Staff Emeritus