- Problem Statement
You place a 4 pound cauliflower on a scale. This lowers scale by 9.6 inches. Gamma = 0.5. From equilibrium, you give the scale a downward velocity of 5 fps.
What kind of damping (or not) occurs?
How many times per min does cauliflower pass equilibrium?
Solve for displacement of cauliflower from equil as fn of time.
- Relevant Equations
- Rcos(wt - d) = 0 (general conversion of sines and cosines to a single cosine minus some phase angle)
Essentially, my question boils down to just part b. My initial thoughts on how to solve this are illustrated above in the second image. To me, I had just interpreted omega, the frequency, as cycles per second. From there, I simply multiplied to get it into minutes. After discussing with a prof. at office hours, he said this is incorrect and is the wrong approach. He noted that what's in the blue (final image on bottom) is the correct approach to part b. This involves considering the period. The explanation was a little rushed (as he had a meeting to attend), and it involved having to do with: the fact that omega isn't just cycles per second, and that setting this equation equal to 0 is done because this is the state of equilibrium. The setting equal to zero makes sense, but I don't see how I'm supposed to know how to interpret omega and I'm actually a little bit shakey on what's in blue so if someone could please clarify this, it would be greatly appreciated.
Thanks for your time.