# Un-dampened vibrating systems, Dynamics

1. Jan 16, 2008

### MightyG

1. The problem statement, all variables and given/known data

having my brain fried with some dynamics problems for uni and my lecturer is on holiday so I dont have anyone to ask.

Currently working on un-dampened vibration and simple harmonic motion and I can work out basic questions such as a weight hanging on a spring but when it starts to involve rotation as well I just cant seem to get my head round it.

this is the type of question I mean:

http://img88.imageshack.us/img88/1142/wtfxr2.jpg [Broken]

any help with this would be greatly appreciated!

3. The attempt at a solution

is there any way of simplifying the problem in a similar way to parallel/series spring problems? or is this too simple a problem to simplify!?!

ive been trying to rethink the problem as a massless wheel of radius L with a tangential downwards force (forcing the wheel clockwise) of WL Sin (theta) and a tangential upwards force (anti-clockwise) of Ka Sin(theta) but im having a hard time trying to work out how to get from the simple free body diagram to a function describing the motion of the system.

am I making fundamental/retarded mistakes or is this the completely wrong way to go about it?

need to try and get my head around these problems asap as ive been told that there is going to be a question almost the exact same as this in my up coming exam!! lol

Last edited by a moderator: May 3, 2017
2. Jan 17, 2008

### CEL

The displacement of the mass is L.sin(theta) and the displacement of the spring a.sin(theta). The momentums to be balanced are m.g.L.cos(theta) and K.a.sin(theta).a.cos(theta).