Question

An oscillator with a mass of 440 g and a period of 0.800 has an amplitude that decreases by 2.20% during each complete oscillation.

If the initial amplitude is 13.2 cm, what will be the amplitude after 31.0 oscillations?

Answer 1

Therefore, the amplitude after 31.0 oscillations is approximately 4.67 cm.

Answer 2

Step-by-step explanation:

The amplitude of an oscillator that decreases by 2.20% during each complete oscillation can be modeled using the equation:

A = A0 * (0.978)^n

where A0 is the initial amplitude, n is the number of oscillations, and 0.978 is the factor by which the amplitude decreases during each oscillation (calculated as 1 - 0.0220).

To find the amplitude after 31.0 oscillations, we can substitute A0 = 13.2 cm and n = 31.0 into the equation:

A = 13.2 * (0.978)^31.0

A = 7.11 cm

Therefore, the amplitude after 31.0 oscillations is 7.11 cm.