Un-dampened vibrating systems, Dynamics

[MightyG]

Homework Statement

having my brain fried with some dynamics problems for uni and my lecturer is on holiday so I don't 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 can't seem to get my head round it.this is the type of question I mean:

http://img88.imageshack.us/img88/1142/wtfxr2.jpg

any help with this would be greatly appreciated!

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 I am 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 I've been told that there is going to be a question almost the exact same as this in my up coming exam! lol

 

[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).

 

[piercas]

Hi there,

It sounds like you are struggling with understanding dynamics and un-dampened vibrating systems. These can be complex topics, so it's understandable that you are having trouble. Firstly, it's important to remember that dynamics deals with the study of motion and forces. In the case of un-dampened vibrating systems, we are looking at systems that have no external forces acting upon them, which means they will continue to vibrate indefinitely.

One way to simplify the problem you mentioned is to think about the forces acting on the system. In this case, we have a weight hanging on a spring, which means the only forces acting on the system are gravity and the spring force. These two forces will balance each other out, resulting in simple harmonic motion. However, when rotation is involved, things become more complicated.

You mentioned trying to think about the problem as a massless wheel with tangential forces acting on it. This is a good approach, but you also need to consider the moment of inertia of the wheel and how it affects the motion. The moment of inertia is a measure of an object's resistance to changes in its rotational motion, and it is affected by the mass distribution and shape of the object.

To solve this type of problem, you will need to use equations of motion for rotational motion, such as Newton's second law for rotation: Στ = Iα, where Στ is the net torque acting on the system, I is the moment of inertia, and α is the angular acceleration. You will also need to consider the relationship between linear and angular variables, such as displacement, velocity, and acceleration.

It's important to practice solving problems like this to become more comfortable with the concepts and equations involved. I would recommend seeking help from a tutor or classmate if your lecturer is unavailable. You can also try looking for online resources or textbooks that provide step-by-step solutions to similar problems. Don't get discouraged, with practice and persistence, you will be able to master these concepts and ace your exam! Good luck!