Problem of Oscillation of mass attached to spring with external force

AI Thread Summary
The discussion focuses on a mass-spring system experiencing forced oscillation due to an external force proportional to cos ωt, where ω is not equal to the natural angular frequency ω0. The governing equations include F = -kx and F = -mω²x, which describe the system's behavior. The solution involves combining the natural frequency dynamics with the external force's influence. Participants suggest referencing textbooks on oscillation or acoustics for deeper insights into forced oscillation problems. Understanding the time displacement of the oscillator requires analyzing the interaction between the spring force and the external force.
Saurabh Sikchi
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Homework Statement


A particle of mass m is attached to a spring (of spring constant k) and has a natural angular frequency ω0. An external force. F(t) proportional to cos ωt(ω ≠ ω0) is applied to the oscillator. The time displacement of the oscillator will be?


Homework Equations


F=-kx
=-mω2x


The Attempt at a Solution


F=-ω02x+F0cos ωt
 
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This is the problem of forced oscillation you can get it in any book on oscillation or acoustics
 

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