Relationship between surface area and damping coefficient

He took the natural log of the amplitude of each oscillation and plotted it against time to obtain a non-linear graph of ln(y) = -λt + ln(A₀). He then plotted the values of λ against the surface area of the card and found a non-linear relationship instead of the expected linear one. The attachment of the card and the geometry of the system may explain this unexpected result. Additionally, the mass of the card may also play a role in the damping. If there is no card attached, the results may be different.
  • #1
kucing
1
0
I have been investigating the damping of an oscillating mass on a spring by a piece of card of varying surface area, in order to work out the damping constant λ for the equation y = A₀ e-λt sin(ωt). I took the natural log of the amplitude of each successive oscillation and plotting that against time elapsed to give a graph of ln(y) = -λt + ln(A₀), so I could take the gradient and obtain a value for λ.

I then plotted a graph of my values for λ against the surface area of the card. I was expecting a linear relationship between λ and surface area, but instead obtained the non-linear graph I have attached.

https://www.physicsforums.com/attachments/screen-shot-2014-11-16-at-20-33-26-png.75536/

Why is this the case? How can I explain this?
 
Last edited by a moderator:
Physics news on Phys.org
  • #2
How exactly is the card attached to the mass? What is the geometry of the system? How does the mass of the card compare to the mass m? What do you get if there's no card attached?

Chet
 

Related to Relationship between surface area and damping coefficient

1. What is the relationship between surface area and damping coefficient?

The relationship between surface area and damping coefficient is that as the surface area of an object increases, the damping coefficient also increases. This means that a larger surface area creates more resistance to motion, resulting in a higher damping coefficient.

2. How does surface area affect damping coefficient?

Surface area directly affects damping coefficient by increasing or decreasing the amount of resistance to motion. A larger surface area means more air or fluid molecules will come into contact with the object, creating more resistance and therefore a higher damping coefficient.

3. Why does surface area affect damping coefficient?

Surface area affects damping coefficient because it determines the amount of fluid or air molecules that come into contact with the object. This contact creates friction, which is responsible for the damping force that opposes the object's motion.

4. Is there a mathematical formula for the relationship between surface area and damping coefficient?

Yes, there is a mathematical formula that describes the relationship between surface area and damping coefficient. It is expressed as: d = bvA, where d is the damping coefficient, b is a constant, v is the velocity of the object, and A is the surface area.

5. How does the relationship between surface area and damping coefficient affect the motion of an object?

The relationship between surface area and damping coefficient affects the motion of an object by creating a damping force that opposes the object's motion. This force decreases the amplitude and velocity of the object's oscillations, resulting in a decrease in its overall motion.

Similar threads

Effect of Surface Area on the Drag Coefficient of a Parachute
    • Introductory Physics Homework Help
Replies
6
Views
2K
Physics IA: Distance B/w Pendulum & Alum. Block, Finding Damping Coefficient
    • Introductory Physics Homework Help
Replies
9
Views
1K
I Why is estimation of ##\frac{Pv}{RT}=1+BP+CP^2+...## interesting?
    • Classical Physics
Replies
2
Views
595
A Practical use of an overall heat transfer coefficient?
    • Thermodynamics
Replies
14
Views
1K
Estimate Decay Coefficient in Ae^-at Graph
    • Introductory Physics Homework Help
Replies
1
Views
896
B Calculating shaded area: I'm getting discrepancies between methods
    • Calculus
Replies
3
Views
376
Difference between resonance in undamped vs damped mass-spring-dashpot
    • Introductory Physics Homework Help
Replies
17
Views
418
I The relationship between reversible and irreversible processes
    • Classical Physics
Replies
5
Views
1K
I Linear regression, feature scaling, and regression coefficients
    • Set Theory, Logic, Probability, Statistics
Replies
8
Views
1K
DIY Vibration Measurement Device for Engineers using Flex Sensors
    • Mechanics
Replies
3
Views
1K

Hot Threads

Recent Insights

Back
Top