A dumped harmonic oscillator of a mass of 500 g has a period of 0.5 second. The amplitude of the oscillation is decreasing 2.0 % during each oscillation. a./ The initial amplitude is 10 cm. What will be the amplitude after 25 oscillation

The answer is below

Explanation:

The amplitude decreases by 2%  during each oscillation. Hence the decrease in amplitude can be represented by an exponential decay in the form:

y = abˣ; where x ad y are variables, a is the initial value and b is the factor.

Let y represent the amplitude after x oscillations. Since the initial amplitude is 10 cm, hence:

a = 10 cm, b = 2% = 0.02.

Therefore:

y = 10(0.02)ˣ

The amplitude after 25 oscillations is gotten by substituting x = 25 into the equation. Hence:

y = 10(0.02)²⁵

y= 3.355 * 10⁻⁴² cm

The amplitude after 25 oscillations is 3.355 * 10⁻⁴² cm