Differential equation for unbalanced rotating force

In summary, the conversation discusses the parameters and equations in the given ODE. The question arises about the meaning of ##m## and its relationship to the other variables in the equation. It is clarified that ##m## represents the mass of the system being described, and that there is no specific figure associated with the problem. The conversation also highlights the importance of considering the physical system that gives rise to the ODE when determining the meaning of its parameters.
  • #1
Dustinsfl
2,281
5

Homework Statement


##M\ddot{y} + k_{eq}y = me\omega^2\sin(\omega t)##

What is ##m##?

Homework Equations

The Attempt at a Solution


In the ODE above, ##M## is the total mass of the problem, correct? For instance, if we had a cantilever beam, ##M = m_b + m_m(0.23)## where ##m_b## is the mass of the beam and ##m_m## is the mass of the motor.

Is ##m## the mass of the motor causing the unbalance or is it the mass of the whole system as well?
 
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  • #2
Is there no figure associated with this problem?

To just start with the ODE given, I think that the only truly correct answer is to say that
m is the 13th letter of the alphabet.

The problem is that there are many physical systems that give rise to a particular describing differential equation. To start with the ODE and ask what the parameters are is pure nonsense.
 

1. What is a differential equation for unbalanced rotating force?

A differential equation for unbalanced rotating force is a mathematical equation that describes the relationship between the unbalanced forces acting on a rotating object and its motion over time. It takes into account factors such as the object's mass, velocity, and the unbalanced forces acting on it.

2. How is a differential equation for unbalanced rotating force different from other types of differential equations?

A differential equation for unbalanced rotating force is specifically used to model the motion of a rotating object due to unbalanced forces. Other types of differential equations may describe different physical phenomena, such as heat transfer or population growth.

3. What are some common applications of differential equations for unbalanced rotating force?

Some common applications of these equations include predicting the motion of spinning objects, analyzing the stability of rotating machinery, and designing control systems for rotating devices.

4. Can differential equations for unbalanced rotating force be solved analytically?

In some cases, these equations can be solved analytically using mathematical techniques such as separation of variables or Laplace transforms. However, in many cases, numerical methods are needed to find solutions.

5. How are differential equations for unbalanced rotating force used in real-world situations?

These equations are used in a variety of real-world situations, such as in engineering and physics, to understand and predict the behavior of rotating systems. They are also used in the development of technology, such as predicting the motion of satellites or designing efficient wind turbines.

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