Question 1179522: I need help with this!!!
A spring oscillates with a frequency of 8 cycles per second. Its initial displacement is 9 centimeters and it's damping factor is 0.3. Give the function, f(t) that describes the position of the spring t seconds after it starts oscillating.
Answer by ikleyn(52803)   (Show Source):
You can put this solution on YOUR website! .
Could you, or your professor, or your textbook, or your other source EXPLAIN what they mean saying "the damping factor" ?
I am asking, because different sources give different definitions (or do not give any definitions, at all).
It looks like, that every school / college / university / (working group) / company has and uses their own definition of this term.
////////////
After intensive search in the Internet, I finally found an adequate definition of the "damping factor" under this link
https://openstax.org/books/precalculus/pages/7-6-modeling-with-trigonometric-equations
and now I am ready to present my solution.
Had damping be zero, the equation of harmonic oscillations would be
x(t) =  .
"9" is the initial displacement; cosine is used due to given initial displacement at the starting moment;
the argument  accounts for the frequency; t is the time in seconds after the start.
Since the dumping 0.3 is imposed, the final formula takes the form
x(t) =  . ANSWER
x(t) is the position coordinate in centimeters relative to the equilibrium.
Solved, answered and explained.
Do not forget to post your "THANKS" to me for my teaching.
``````````````
From your comments, I noticed that you are familiar with the computer system SASSY.
Where and how did you get familiarity with it ?
I worked several years with this system on different engineering projects . . .
And even participated in creating the Manual on this system, after all . . .
|
|
|
