Simple Harmonic Motion and Damping

In summary, the term used to describe a system with just enough damping to stop oscillations is "critical damping". This occurs when the resistive forces are balanced to prevent oscillation. Automobile shock absorbers are typically designed to be slightly underdamped, providing a balance of good ride quality and quick responses. Overdamping would result in a rough ride while underdamping allows for oscillations and a softer ride.
  • #1
SnackMan78
5
0
Textbook Question:

Which one of the following terms is used to describe a system in which the degree of damping is just enough to stop the system from oscillating?

a) Slightly damped
b) Underdamped
c) Critically damped
d) Overdamped
e) Resonance


Textbook says that the smallest degree of damping that completely eliminates the oscillation is termed "critical damping". (This example has no picture to illustrate it.) Then a couple of lines later in the textbook, "Typical automobile shock absorbers are designed to produced underdamped motion somewhat like that in curve 3. (an illustration that highlights the best scenario of the motions: underdamped and undamped motion)

My answer is C based on the first textbook example, but I want to get confirmation from others. The shock absorber and underdamped line of text is somewhat confusing. Any other thoughts?
 
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  • #2
(c) is correct. Critical damping occurs when the resistive forces are 'just enough' to prevent an ocsillation as you say. Most motor car shock absorbers are made slightly underdamped, this still gives a good ride without too much 'boucing' but also gives the car quicker responses.

-Hoot
 
  • #3
You should realize that to physically make something critically damped is impossible. It aint going to happen. That then leaves the option of over or underdamping. Over damping would cause a pretty rough ride. It would be pretty rigid. If it is underdamped, that allows an oscillation, but results in a softer ride. The idea is to not be too much underdamped.

You are corrct with C as Hoot has said.
 

1. What is simple harmonic motion?

Simple harmonic motion refers to the back and forth motion of an object around an equilibrium point, where the acceleration of the object is directly proportional to its displacement from the equilibrium point and is directed towards the equilibrium point.

2. What is the formula for calculating the period of simple harmonic motion?

The formula for calculating the period of simple harmonic motion is T = 2π√(m/k), where T is the period, m is the mass of the object, and k is the spring constant.

3. How does damping affect simple harmonic motion?

Damping refers to the gradual decrease in the amplitude of oscillation in simple harmonic motion. It can be caused by external factors such as friction or air resistance. Damping results in a decrease in the period and amplitude of the motion.

4. What is the difference between underdamped, overdamped, and critically damped systems?

In an underdamped system, the damping force is less than the critical damping force, resulting in oscillations that gradually decrease in amplitude. In an overdamped system, the damping force is greater than the critical damping force, resulting in slow and smooth motion towards the equilibrium point. In a critically damped system, the damping force is equal to the critical damping force, resulting in the fastest approach to the equilibrium point without any oscillations.

5. How is simple harmonic motion related to resonance?

Resonance occurs when the frequency of an external force matches the natural frequency of an object. In simple harmonic motion, the natural frequency of an object is directly related to its mass and spring constant. When an external force with the same frequency as the natural frequency is applied to the object, it experiences maximum amplitude and can lead to damaging effects.

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