Which parameter determines the oscillation frequency in the absence of damping?

• A. Normal Frequency (Wo)
• B. Damping Factor
• C. Rise Time
• D. Settling Time

Answer: (A)

When there is no damping, the system behaves as a pure harmonic oscillator. Its motion is governed by x'' + ω_n^2 x = 0, whose solution is a combination of sine and cosine terms with angular frequency ω_n. That means the oscillation rate—the frequency of the oscillations—is set by the natural (undamped) frequency ω_n, also called the normal frequency. The period is T = 2π/ω_n, so ω_n directly fixes how fast the oscillations occur.

The damping factor controls how quickly the oscillations die away; with zero damping there is no decay, so it doesn’t determine the oscillation rate. Rise time and settling time describe how the system responds over time toward its final value and depend on both ω_n and damping, but they are not the fundamental parameter that fixes the oscillation frequency in the undamped case.