Angular Frequency of Spring Mass System: Explained

AI Thread Summary
The angular frequency of a spring-mass system is defined as the rate of oscillation in radians per unit time, despite the system's one-dimensional motion. The time period of the system is given by T = 2π(m/k)^(1/2), which relates to the angular frequency through the equation ω = 2π/T. While the term "angular frequency" may seem misleading, it effectively describes the sinusoidal nature of the motion, represented by A sin(ωt). The ωt term can be interpreted as an angle, even though it does not correspond to a physical angle. Understanding this concept is essential for grasping the dynamics of oscillations in spring-mass systems.
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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.
 
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Help please, I'm new to oscillations and waves.
 
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.
 
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