Mathematics
Mathematics
Problem
A damped oscillator loses 20% of its energy on each oscillation. When the oscillator's energy has been reduced to below 1% of its initial energy, how many oscillations will it have completed? a. 4 b. 5 c. 21 d. 41Intuitive explanation
The key insight is that energy decays exponentially with each cycle—after oscillations, the remaining energy is . You need to find when this drops below 1% of the starting value, which means solving an inequality involving logarithms. Think of it as asking: how many times do you multiply by 0.8 before the result falls below 0.01?
Intuitive explanation
The key insight is that energy decays exponentially with each cycle—after oscillations, the remaining energy is . You need to find when this drops below 1% of the starting value, which means solving an inequality involving logarithms. Think of it as asking: how many times do you multiply by 0.8 before the result falls below 0.01?