Phasor representation for a mass and spring

In summary, the conversation discusses the Fourier representation for a spring-mass system and the relationship between force and velocity in the frequency domain. It is noted that while the physical behavior of the system follows the expected pattern of the force leading the velocity for a mass system and lagging for a spring system, the mathematical representation may appear different due to the complex equations involved. The Fourier representation is a useful tool for analyzing system behavior, but it may not always directly reflect the physical behavior of the system.
  • #1
Radel
6
0
Hi,

While writing the Fourier representation for the spring-mass system, we have the equation:
(-jωm+B-S/jω).U(jω)=F(jω) with F,U,m,B and S being the force, velocity,mass, damping coefficient and spring constant respectively.

From this equation, is it right to infer that :
1) Force lags the velocity as F'(jω)= (-jωm) . U(jω)
2)Force leads velocity as F'(jω)= (jS/ω). U(jω)

However, physically the above argument doesn't seem to be correct. As force leads the velocity for a mass system and force lags velocity for a spring system.

So could someone please correct me the mistake in my understanding.
 
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  • #2


Hello,

Thank you for your post. You are correct in your understanding that the force leads the velocity for a mass system and lags for a spring system. This can be seen in the equations you have provided, where the term (-jωm) represents the force and the term (jS/ω) represents the velocity.

The reason for this discrepancy is due to the fact that the Fourier representation is a mathematical tool used to analyze the behavior of a system. It is not always a direct representation of the physical behavior of the system. In this case, the Fourier representation is showing the relationship between the force and velocity in the frequency domain, rather than in the time domain.

In the time domain, we would see that the force leads the velocity for a mass system and lags for a spring system, as you correctly stated. However, in the frequency domain, the relationship between the two quantities may appear different due to the complex nature of the equations.

I hope this helps to clarify your understanding. If you have any further questions, please feel free to ask. Keep up the good work!
 

1. What is a phasor representation?

A phasor representation is a graphical method used to represent the amplitude and phase of a sinusoidal function. It is commonly used in the study of oscillating systems, such as a mass and spring, to analyze the behavior of these systems over time.

2. How is a mass and spring system represented using phasors?

A mass and spring system can be represented using a phasor diagram, where the amplitude of the oscillation is represented by the length of the phasor and the phase is represented by the angle of the phasor. The phasor rotates counterclockwise with time, representing the oscillation of the system.

3. What is the significance of phasor representation for a mass and spring system?

Phasor representation allows for a simplified analysis of the behavior of a mass and spring system. It provides a visual representation of the amplitude and phase of the oscillation, making it easier to understand and predict the behavior of the system over time.

4. Can phasor representation be used to solve problems involving a mass and spring system?

Yes, phasor representation can be used to solve problems involving a mass and spring system. It allows for the application of mathematical principles, such as vector addition and trigonometric functions, to analyze the system and determine its behavior.

5. Are there any limitations to using phasor representation for a mass and spring system?

Phasor representation is most useful for analyzing systems with simple harmonic motion, where the amplitude and frequency of the oscillation remain constant. It may not be as effective for more complex systems with varying amplitudes and frequencies.

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