A mass–spring oscillator is released with an initial amplitude of
MATHEMATICS · Subjective · A Level · Mathematics · Sequences and series · Sequences and series
Problem
A mass–spring oscillator is released with an initial amplitude of 6cm. Measurements show that after every complete oscillation the amplitude becomes 95% of its value at the start of that cycle.
(a) Calculate the amplitude after the oscillator has completed 5 full oscillations.
(b) Mechanical energy of such an oscillator is proportional to the square of its amplitude. Determine the percentage of the initial mechanical energy still remaining after 5 oscillations.
(c) Based on your result in part (b), comment whether the loss of energy with time is more consistent with a linear decay or an exponential decay. Give one reason to support your conclusion.