Question

A damped harmonic oscillator consists of a mass on a spring, with a small damping force that is proportional to the speed of the block. If the mass of the block is 320 g, the period of oscillation is 2.4 s, and the block loses 10% of its mechanical energy after one cycle, what is the damping constant?

Answer 1

The damping constant for the given damped harmonic oscillator with a period of 2.4 s and 10% energy loss per cycle is approximately -0.105.

Step-by-step explanation:

The damping constant, also known as the damping coefficient, can be calculated using the formula:

damping constant = (ln(final amplitude / initial amplitude)) / (2 * pi * number of cycles)

In this case, the block loses 10% of its mechanical energy after one cycle, which means the final amplitude is 90% of the initial amplitude. Substituting the values into the formula:

damping constant = (ln(0.9)) / (2 * pi * 1)

damping constant ≈ -0.105