Damped simple harmonic motion

  • Thread starter erisedk
  • Start date
  • #1
374
7

Homework Statement


The amplitude of a simple pendulum oscillating in air with a small spherical bob, decreases from 10 cm to 8 cm in 40 seconds. Assuming that Stokes Law is valid, and ratio of the coefficient of viscosity of air to that of carbon dioxide is 1.3, the time in which amplitude of this pendulum will reduce from 10 cm to 5 cm in carbon dioxide will be close to (ln 5 = 1.601, ln 2 = 0.693)

Homework Equations


x(t) = Ae-bt/2m cos(ωt + Φ)

The Attempt at a Solution


I suppose that b ∝ viscosity
So, assuming b/2m = k
8 = 10e-k×40 ------- (1)
5 = 10e-k×t/1.3 ---------- (2)
Dividing 1/2 --
8/5 = ekt/1.3 - 40k

I have no idea what to do beyond this, I haven't been given values for b or m. Also, my solution may be very wrong because I'm not sure about this at all.
 

Answers and Replies

  • #2
ChrisVer
Gold Member
3,381
462
why did you divide [1] by [2]?
 
  • #3
374
7
Oh my god, this is embarrassing. Got it, two equations, two unknowns. Thank you :D
 
  • #4
using equation 1 , find k value and put that in equation 2 to find the value of time
 

Related Threads on Damped simple harmonic motion

  • Last Post
Replies
10
Views
2K
Replies
4
Views
8K
  • Last Post
Replies
2
Views
6K
  • Last Post
Replies
2
Views
713
Replies
8
Views
3K
Replies
1
Views
1K
  • Last Post
Replies
0
Views
4K
  • Last Post
Replies
4
Views
384
  • Last Post
Replies
3
Views
815
  • Last Post
Replies
2
Views
10K
Top