Underdamped

Definition

An underdamped system is one where the damping force is not strong enough to prevent oscillations. It results in oscillatory motion with gradually decreasing amplitude over time.

5 Must Know Facts For Your Next Test

1. An underdamped system has a damping ratio less than 1.
2. The oscillations in an underdamped system are characterized by an exponential decay envelope.
3. The frequency of oscillation in an underdamped system is called the damped natural frequency, which is lower than the undamped natural frequency.
4. Examples of underdamped systems include certain types of car suspension systems and electrical circuits with resistance, inductance, and capacitance.
5. $x(t) = e^{-\zeta \omega_n t} (A \cos(\omega_d t) + B \sin(\omega_d t))$ describes the displacement over time for an underdamped oscillator, where $\zeta$ is the damping ratio and $\omega_d$ is the damped natural frequency.

Review Questions

• What is the damping ratio for an underdamped system?
• How does the amplitude change over time in an underdamped system?
• Compare the damped natural frequency to the undamped natural frequency in an underdamped oscillator.

Related terms

Overdamping: Occurs when the damping force is strong enough to prevent oscillations, resulting in a slow return to equilibrium without overshooting.

Critical Damping: The exact amount of damping that results in the fastest return to equilibrium without oscillating.

Damping Ratio: A dimensionless measure describing how oscillations in a system decay after a disturbance, defined as the ratio of actual damping to critical damping.