Forced vibrations of damped single degree freedom systems?

In summary, a spring mass damper system subjected to a periodic force only depends on the force and ignores the restoring forces caused by the spring. In a damped free vibration, the mass vibrates at the damping frequency and eventually the amplitude vanishes. However, in a forced vibration with damping, the mass vibrates at the frequency of the periodic force. It is unclear what happens to the oscillations caused by the damper in under damping, as they are said to die out quickly but should still oscillate a few times before completely dying out. It is also unclear how the mass can vibrate at two frequencies (damping and periodic force) simultaneously. The provided Wikipedia page may provide further clarification.
  • #1
firecool
11
0
in a spring mass damper system subjected to a periodic force. the response of the system only depends on the force and the restoring forces caused due to the spring is ignored because the damper is assumed to have taken care of it. now it's here that my confusion originates. in a damped free vibration (under damping) when a initial displacement is given to the mass, the mass vibrates at a damping frequency and the amplitude eventually vanishes. the mass completes a few oscillations before the vibration completely dies out.
but in a forced vibration with damping, when the force is applied the vibrations take place at the frequency of the periodic force, so what happens to the oscillations caused due to the damper(in under damping). in my book says those vibrations due to damping die out quickly, but they atleast need to oscillate atleast 2-3 times before dying out, and how can they do that while the periodic force is still being applied. how can the mass vibrate at two frequencies( damping and periodic force's) at the same time?
 
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  • #2
I'm sorry I don't really understand your question but have a read of this wikipedia page (in case you haven't done so already):

http://en.wikipedia.org/wiki/Damping

Hope it helps!
 

1. What is a "forced vibration" in a damped single degree freedom system?

In a damped single degree freedom system, a forced vibration refers to the motion of the system that is caused by an external force or input. This external force can be periodic or non-periodic, and the system responds by oscillating at a specific frequency.

2. How is damping effect taken into account in forced vibrations of single degree freedom systems?

Damping effect in forced vibrations of single degree freedom systems is typically represented by a damping coefficient, which reflects the energy dissipation in the system. This coefficient is used in the equation of motion to calculate the response of the system to the external force.

3. What is a single degree freedom system?

A single degree freedom system refers to a mechanical system that has only one independent coordinate or degree of freedom. This means that the motion of the system can be described by a single variable, such as displacement or angle.

4. How do we analyze forced vibrations of damped single degree freedom systems?

The analysis of forced vibrations of damped single degree freedom systems involves solving the equation of motion, which takes into account the external force, damping effect, and stiffness of the system. This can be done using analytical methods, such as the method of undetermined coefficients, or numerical methods, such as the finite element method.

5. What are the practical applications of forced vibrations of damped single degree freedom systems?

Forced vibrations of damped single degree freedom systems are commonly seen in engineering and mechanical systems, such as bridges, buildings, and machines. Understanding and analyzing these vibrations is important for designing and maintaining these structures and ensuring their safety and efficiency.

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