Question

A spring-mass-damper system (m = 10 kg, k = 17400 N/m) has natural frequency 13.2 rad/s. Find the damping coefficient $c$ for critical damping (round off to nearest integer).

Hint:

Remember: critically damped systems use $c_c = 2\sqrt{km}$.

Answer 1

Correct Answer: 833

The natural frequency is:
\[ \omega_n = \sqrt{\frac{k}{m}}. \] Given \( \omega_n = 13.2 \):
\[ 13.2 = \sqrt{\frac{17400}{10}} = \sqrt{1740} \approx 13.19 \ (\text{correct}). \] Critical damping coefficient:
\[ c_c = 2 \sqrt{k m} = 2 \sqrt{17400 \times 10} = 2 \sqrt{174000} \approx 2 \times 417.0 \approx 834. \] Rounded to nearest integer: \[ c = 834 \text{ Ns/m}. \]