A Primer on Sinusoidal Vibration

September 15, 2023

In this “Ask Joel” series of videos, we will learn about the shape of a sine wave and resonance as it pertains to vibration testing.

Frequency & Period

A basic mass-spring mechanical system can help illustrate the basics of sine vibration characteristics. Spring oscillations are sinusoidal. They are characterized by the time to complete one cycle (period) or the number of cycles that occur in one second (frequency). The period and frequency have an inverse relationship, which this video demonstrates in the VibrationVIEW software.

Learn more: Introduction to the Sine Wave

Hooke’s Law

Hooke’s Law is a principle foundational to the vibration testing industry. It describes the relationship between the force applied to an ideal mass-spring system and how far the system extends.


Every object has a unique natural frequency (or frequencies) due to its material properties. Resonance occurs when an object is forced to vibrate at its natural frequency. This video demonstrates a sine sweep to illustrate the resonance of an object on a shaker.

Learn more: Basics of Vibration Resonance

Measuring Resonance


Amplitude is another vibration measurement that relates to resonance. Resonances are characterized by a peak or maximum value measured from its zero value. In addition to amplitude, this video examines the characteristics of resonance on a transmissibility graph.

Bandwidth/Q value

Resonance can occur rapidly, meaning over a tight range of frequencies. The bandwidth and Q factor (or quality factor) measure how quickly a resonance occurs.

Learn more: Introduction to Resonance

Mass Loading

Mass loading is the effect of adding mass to a vibrating object. An accelerometer, which measures signal acceleration, has a mass value and changes the property of the vibration object it measures. One result of mass loading is a lower resonant frequency of the object.


The period, frequency, and amplitude define the shape of a sine wave. Phase is another relevant measurement of a sine wave, which indicates where the sinusoid is in its cycle in degrees or radians. Vibration test engineers typically compare the relative phases of two signals.

Learn more: Phase of a Sine Wave