What is the Damping Coefficient in a Pendulum's Dampened Oscillation?

[GreenLantern674]

[SOLVED] Dampened Oscillations Problem

A pendulum of length 1.00 m is released from an initial angle of 15.0°. After 1200 s, its amplitude is reduced by friction to 5.5°. What is the value of b/2m?

How do you do this one? I know it has something to do with the formula w= sqrt(W0^2 - (b/2m)^2). I tried plugging in sqrt(g/L) for W0, but I don't know what to use for the first w.

 

[GreenLantern674]

Never mind. It turns out I was using the wrong formula.

 

[ogb p]

The dampened oscillations problem is a classic example of how friction can affect the behavior of a pendulum. In this case, the initial angle and length of the pendulum are known, but the value of b/2m needs to be determined. This value represents the damping coefficient divided by twice the mass of the pendulum.

To solve this problem, we can use the formula for the angular frequency of a dampened oscillation, which you have correctly identified as w= sqrt(W0^2 - (b/2m)^2). Here, W0 represents the natural frequency of the pendulum, which can be calculated using the formula W0= sqrt(g/L), where g is the acceleration due to gravity and L is the length of the pendulum.

To find the value of b/2m, we can rearrange the formula to b/2m= sqrt(W0^2-w^2). Since we know the initial angle and amplitude after 1200 seconds, we can calculate the angular frequency using the formula w= (initial angle - final amplitude)/time. Plugging in all the known values, we can solve for b/2m and get the answer to the problem.

In summary, the dampened oscillations problem is a great example of how mathematical formulas can be used to understand and solve real-world problems in physics. By applying the appropriate formula and using known values, we can determine the value of b/2m and fully understand the behavior of the pendulum in this scenario.