Underdamped response

Tags

• Electronics
• physics
• Electronics formula
• physics formula
• rlc
• Second-order RLC circuits

Detail

Explore the idea

Variables

• $\omega_0,\omega_d$frequencies (rad/s)
• $\alpha$damping (s^{-1})
• $\zeta,Q$dimensionless
• $R,L,C$Ω, H, F.

Conditions

• Linear RLC; positive R, L and C.

Intuitive explanation

For “Underdamped response”: ζ compares α with ω0 and decides two exponentials, the boundary, or a damped oscillation.

Worked example

Common mistakes

• confusing α with ω0
• classifying ζ with inconsistent R, L, C
• dropping the 2 in α=R/(2L)

Frequently asked questions

What must be checked before using the Underdamped response relation?

Compute α and ω0 with the same R, L, C and classify ζ before writing v(t).

Also known as

• damping, zeta, natural frequency, underdamped oscillation

Conventions

• rad/s or dimensionless according to the left-hand side

Related formulas

• Related

  Critically damped response

  $$\zeta=1$$
  Open formulaOpen in section

• Related

  Damped natural frequency

  $$\omega_d=\omega_0\sqrt{1-\zeta^2}$$
  Open formulaOpen in section

• Related

  Energy stored in a capacitor

  $$w_C=\frac{1}{2}Cv^2$$
  Open formulaOpen in section

• Related

  Energy stored in an inductor

  $$w_L=\frac{1}{2}Li^2$$
  Open formulaOpen in section