Final answer:
To find the damping factor of the oscillator, we can use the formula for the period of an oscillator with damping. Given the initial and final periods, we can set up an equation and solve for the damping factor.
Step-by-step explanation:
To find the damping factor of the oscillator, we can use the formula for the period of an oscillator with damping, which is:
T = 2πα/(δω)
Where T is the period, α is the damping factor, and εω is the angular frequency.
Given that the initial period is 1.500 s and the final period is 1.501 s, we can set up the following equation:
1.500 = 2πα/(εω)
1.501 = 2πα/(εω)
By subtracting the two equations, we can eliminate εω and solve for α:
0.001 = 2πα/(εω)
εω = 2πα/0.001
εω = 2000πα
Substituting this value back into the original equation, we can solve for α:
1.500 = 2πα/2000πα
1.500 = 1/2000
α = 1/2000