How Do You Calculate the Damping Coefficient of a Pendulum in Water?

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To calculate the damping coefficient (C) of a pendulum in water, the equation of motion is given as θ'' + (c/m)θ' + (g/l)θ = 0. The user has provided parameters: mass (M) of 1 kg, length (L) of 1.0 m, and a period (T) of 2.02 seconds. The natural frequency (Wn) can be calculated using Wn = sqrt(g/L). The discussion suggests that the half-life formula T(1/2) = LN(2)/λ may not be applicable in this context, and emphasizes the importance of using the correct equations for solving the motion of the pendulum. Understanding the method to solve the differential equation is crucial for finding the damping coefficient.
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I am giving M=1kg, L=1.0m, T(period) = 2.02sec. I need to find C

The pendulum is in water.

The eq of motion is double-dot-theta+(c/m)single-dot-theta+(g/l)theta = 0

I was doing some research and found this half life formula...T(1/2) = LN(2)/ Lamda. I am not sure where to go from here...

I know Wn = sqrt(g/L)...
 
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math111 said:
I am giving M=1kg, L=1.0m, T(period) = 2.02sec. I need to find C

The pendulum is in water.

The eq of motion is θ'' + (c/m)θ' + (g/l)θ = 0

I was doing some research and found this half life formula...T(1/2) = LN(2)/λ. I am not sure where to go from here...

I know Wn = sqrt(g/L)...

Hi math111! :smile:

(have a theta: θ and a lamda: λ and use ' instead of dot :smile:)

hmm … I'm don't think that T(1/2) is the same T that you were given. :confused:

It is not a good idea to trawl the web looking for an equation that might fit. :frown:

Hint: do you know any method of solving θ'' + (c/m)θ' + (g/l)θ = 0 ? :smile:​
 

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