Natural frequency, damping ratio and steady state amplitude help needed

In summary, the conversation discusses a mass of 3.0 kg suspended from a vertical spring with a static deflection of 60 mm and subjected to viscous damping of 36 N s/m. The value of the natural frequency in Hz and rad/s, damping ratio, and steady state amplitude of oscillations are to be calculated. The question also mentions a periodic force of amplitude 10 N and frequency of 1.5 Hz acting on the mass. Further clarification and help is requested as the answerer is unsure of how to proceed.
  • #1
CovenK
1
0
(1) A mass of 3.0 kg is suspended from a vertical spring and produces a static deflection of 60 mm.
The system is also subjected to viscous damping of 36 N s/m.

Calculate the value of the:

(a) natural frequency
i. In Hz
ii. And rad/s

(b) damping ratio

(c) and what will be the steady state amplitude of the oscillations produced when the mass is acted on by a periodic force of amplitude 10 N and frequency 1.5 Hz?


I really don't know how to answer this question, and would appreciate any help if possible.
Many thanks in advance.
 
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  • #2
Hi CovenK, welcome to physicsforums :) um, usually people are meant to have done some of the working for the problem before asking for help on the forum. What is it you are stuck on? Have you tried any equations? Maybe the best place to start is to look in the textbook for similar physical situations, and look up the physics words which are in the question.
 

1. What is natural frequency in relation to oscillation?

Natural frequency refers to the frequency at which an object or system vibrates in its natural state without any external forces acting on it. It is determined by the stiffness and mass of the object or system.

2. How does damping ratio affect the amplitude of oscillation?

Damping ratio is a measure of how quickly the amplitude of an oscillating system decreases over time. A higher damping ratio means the amplitude decreases more rapidly, while a lower damping ratio results in a slower decrease of amplitude.

3. What is the relationship between natural frequency and damping ratio?

Natural frequency and damping ratio are inversely related. As the natural frequency of a system increases, the damping ratio decreases. This means that a higher natural frequency results in a longer period of oscillation.

4. How do I calculate the steady state amplitude of an oscillating system?

The steady state amplitude of an oscillating system can be calculated using the formula A = F0/(2mωn√(1-ζ²)), where A is the amplitude, F0 is the driving force, m is the mass, ωn is the natural frequency, and ζ is the damping ratio.

5. How can I use natural frequency, damping ratio, and steady state amplitude to analyze and control oscillation in a system?

By understanding the natural frequency and damping ratio of a system, engineers and scientists can design and implement control measures to minimize or amplify the amplitude of oscillation. This can be crucial in preventing structural damage or optimizing performance in various applications.

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