Final answer:
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