Amplitude and Natural Frequency of an Unbalanced Motor System

[bikramjit das]

Homework Statement

Question:There is a fixed end beam PQ. It is carrying a motor M. The motor is unbalanced and when the motor is rotating ,it is making the beam to vibrate with a frequency equal to the speed of the motor. A small mass is kept at point A just above the motor on the beam. it also goes up & down along with the beam . When the motor speed is 120 - 150rpm, the object at A is loosing contact with the beam & is actually dancing on the beam. Determine the amplitude of vibration when the speed of motor is 120 rpm and when 150 rpm . Then calculate the natural frequency of the system.

 

[gneill]

What have you tried or thought about so far?

 

[bikramjit das]

I think I can put the concept of whirling shaft in it... so I put the formula for amplitude as , y=e / (_{}Wn / _{}W )^2 -1

 

[bikramjit das]

pls help me and tell whether it is correct or not

 

[gneill]

I don't know if your approach can achieve results. When I see a vibrating beam I tend to think of simple harmonic motion (SHM). And a beam that's being driven by a motor (sine function) would be forced SHM.

 

[bikramjit das]

so, in this kind of forced SHM , what will be the eqn of motion?? pls try to do this question once.. I have been trying it from many days

 

[gneill]

so, in this kind of forced SHM , what will be the eqn of motion?? pls try to do this question once.. I have been trying it from many days

The forum rules don't allow direct answering of problems. The idea is to give just enough help so that the problem poser can solve it him/herself.

That said, all SHM has a single form of differential equation. The solutions tend to be sinusoidal in nature. Have a look at the http://en.wikipedia.org/wiki/Harmonic_oscillator" .

You're going to want to think about under what conditions, given SHM, the mass will just begin to lose touch with the oscillating beam.

 

[bikramjit das]

this link didn't helped at all sir... pls give the diff eqn at least

 

[gneill]

The differential equation for the sinusoidally driven SHM is given in the link in the section, "Sinusoidal driving force".

 

[berkeman]

Homework Statement

Question:There is a fixed end beam PQ. It is carrying a motor M. The motor is unbalanced and when the motor is rotating ,it is making the beam to vibrate with a frequency equal to the speed of the motor. A small mass is kept at point A just above the motor on the beam. it also goes up & down along with the beam . When the motor speed is 120 - 150rpm, the object at A is loosing contact with the beam & is actually dancing on the beam. Determine the amplitude of vibration when the speed of motor is 120 rpm and when 150 rpm . Then calculate the natural frequency of the system.

The problem seems to need more description, doesn't it? Like the mass that the motor is spinning, the stiffness and length of the shaft, and so on. SHM usually deals with spring forces and masses.

You also need more mechanical details about the motor and how it attaches to the stationary shaft. Why would it start to dance on the beam? What is physically separating?

Can you scan the problem drawing from your assignment?

And as gneill correctly points out, we will not be doing your work for you on this. We are happy to try to help you figure out how to solve the problem, though.


EDIT -- Oh, maybe they are saying that the mass is just resting on the top of the beam, and they want to know when the mass loses contact with the beam as it oscillates in its fundamental mode. That may simplify the problem a bit, but I'm not sure how much.