Damped Simple Harmonic Motion: Finding Amplitude Reduction in Carbon Dioxide

[erisedk]

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 = e^{kt/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.

 

[ChrisVer]

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

 

[erisedk]

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

 

[harshitha j]

using equation 1 , find k value and put that in equation 2 to find the value of time