Question

An oscillator with a mass of 470 g and a period of 0.600 s has an amplitude that decreases by 1.30% during each complete oscillation.

If the initial amplitude is 7.60 cm , what will be the amplitude after 37.0 oscillations?

Answer 1

Solution:

Reducing something by 1.3% is the same as multiplying it by (1 - 1.3/100) = 0.987

(This is a basic maths 'trick', but if you are not familiar with it, here's an explanation.
Suppose you reduce something (call it X) by P%.
P% of X = (P/100)X
If X is reduced by this amount, the new value = X - (P/100)X
=X(1 - P/100)
In this problem P=1.3%, so the factor (1-P/100) = 1 - 1.3/100 = 0.987)

1)
After 1 oscillation the amplitude is reduced by 0.987. After 2 oscillations it will be reduced again by 0.987². So after 37 oscillations it will be reduced by a factor 0.987³⁷

New amplitude = 7.60 x (0.987³⁷) = 4.68cm

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