In a mass–spring system, the symbol f represents which physical quantity?

• A. The total energy
• B. The damping coefficient
• C. The number of cycles per unit time
• D. The maximum displacement

Answer: (C)

The quantity f is the rate at which the mass completes cycles of motion—the frequency. It tells you how many full oscillations happen in one second, so f = 1/T where T is the period between identical points in the motion. For a simple mass–spring oscillator, the frequency (ignoring damping) depends on the spring constant and the mass as f = (1/2π)√(k/m), with the angular frequency related by ω = 2πf. The other quantities describe energy, damping, or amplitude, not how often the cycles occur. Thus f represents the number of cycles per unit time.