Answer to Question #179195 in Classical Mechanics for Hadi

Question

The amplitude of a lightly damped oscillator decreases by 3.0% during each cycle.After how many oscillations(approximately) will the amplitude drop to its half its initial value

Answer 1

$\frac A2=A(1-\frac{k}{100})^n,$

$\frac 12=(1-\frac{k}{100})^n,$

$n=\frac{1}{log_2\frac{100}{100-k}}=23.$