Simple Harmonic Motion – Identifying the Quantity Measured in Cycles Per Second For a body executing simple harmonic motion (SHM), the number of cycles completed per second is called:

Introduction / Context:
Terminology in vibrations is precise and must not be confused. In simple harmonic motion, the key measurable quantities are amplitude, period, and frequency. Frequency dictates how many complete cycles occur per unit time and is fundamental in structural dynamics, seismology, and machine design.

Given Data / Assumptions:

• Sinusoidal or harmonic motion about an equilibrium position.
• Constant amplitude and frequency for ideal SHM.
• No damping or external forcing considered.

Concept / Approach:

Frequency f is defined as cycles per second (hertz). The period T is the time for one complete cycle, with f = 1 / T. Amplitude A is the maximum displacement from equilibrium, independent of f in ideal linear SHM. Beats arise from superposition of close frequencies, not from a single harmonic oscillator.

Step-by-Step Solution:

Verification / Alternative check:

In a mass–spring system with natural circular frequency ω_n, frequency f = ω_n / (2π), and period T = 2π / ω_n. The interpretation remains consistent for pendulums and other linear SHM systems for small oscillations.

Why Other Options Are Wrong:

(a) 'Oscillation' refers to the motion itself, not a rate. (b) Amplitude is a displacement magnitude. (c) Period is time per cycle, not cycles per second. (d) Beats occur from superposition of two different frequencies.

Common Pitfalls:

Interchanging period and frequency; using 'oscillation' as a unit-bearing quantity.

Final Answer:

Frequency