An oscillator with a mass of 520 g and a period of1.2 s has an amplitude that decreases by 2.20% during each complete oscillation.

Question

At what time will the energy be reduced to 15.0% of its initial value?

Answer 1

The number of oscillations required, N, must satisfy

(1-.022)^N = (0.978)^N = 0.15
N ln 0.978 = ln 0.15
N = 85.3

The time required is N * 1.2 s = 102 seconds.

Answer 2

why is the second part incorrect

Answer 3

I misread the problem. I calculated the time it takes the AMPLITUDE to decrease to 15% of its initial value. The ENERGY reaches 15% of the initial value when the amplitude has reached sqrt(0.15) or 38.7% of the initial value. The requires half the number of oscillations and half the time of my previous answer,
N ln(0.978) = ln(0.387)
N = 42.7
t = 51 seconds