# Damped simple harmonic motion

1. Feb 5, 2016

### erisedk

1. The problem statement, all variables and given/known data
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)

2. Relevant equations
x(t) = Ae-bt/2m cos(ωt + Φ)

3. 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.

2. Feb 5, 2016

### ChrisVer

why did you divide [1] by [2]?

3. Feb 5, 2016

### erisedk

Oh my god, this is embarrassing. Got it, two equations, two unknowns. Thank you :D