Angular Frequency of Spring Mass System: Explained

[sArGe99]

Homework Statement

Now, I've learned that the time period of a spring mass system having spring constant k and mass m is 2 \pi (m/k)^1/2. What is actually the angular frequency of a vertical spring mass system. It is executing one-dimensional motion, how does it have angular frequency? And..don't we call it angular velocity rather than angular frequency?

Homework Equations

T = 2 \pi (m/k)^1/2

The Attempt at a Solution

Checked a few books, none of them really explained it.

 

[sArGe99]

Help please, I'm new to oscillations and waves.

 

[Redbelly98]

This is actually a good question, though I've never heard anyone ask it before.

Angular frequency is somewhat a misnomer. But it has come to mean the frequency (in terms of radians) of anything that oscillates sinusoidally.

Since spring - mass motion is described by

A sin(ωt),​

then the ωt term can be thought of as an angle--even though it doesn't represent the angle of any physical object.