Question

The discharge of a capacitor through a ballistic galvanometer produces a damped frequency of 0.125 Hz and successive swings of 120, 96 and 76.8 mm. The damping ratio is?

(a) 0.0568

(b) 0.0887

(c) 0.0357

(d) 0.0441

The question was posed to me in an online quiz.

This interesting question is from Advanced Problems on Indicating Instruments in portion Extension of Instrument Ranges of Electrical Measurements

Answer 1

The correct answer is (c) 0.0357

The best explanation: Logarithmic decrement, δ = \(ln \frac{x_1}{x_2} = ln \frac{120}{96}\) = 0.225

Now, δ is related to damping ratio K as, K = \(\frac{1}{(1 + (\frac{2π}{δ})^2)^{0.5}}\)

K = \(\frac{1}{(1 + (\frac{2π}{0.225})^2)^{0.5}}\)

∴ K = 0.0357.