Abstract
The simple harmonic vibration, damping vibration and forced vibration of an oscillator attached to the massless spring are always discussed in general mechanics courses. In this article, we focus on the heavy-spring conditions. We first investigate the general situation where both viscous resistance and applied force are considered under the perspective of the renormalization group theory. Then we use analytic method to study the damped oscillation of an oscillator attached to the heavy spring, where renormalization method fails to work.
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