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Stopping oscillations of a simple harmonic oscillator using an impulse force. (English) Zbl 1416.34012

Summary: The harmonic oscillator is famously used among many systems to model the motion of a mass-spring system. A neither damped nor driven harmonic oscillator is known as a simple harmonic oscillator. Its solution commonly known as simple harmonic motion comprises of continuous sinusoidal oscillations with a constant amplitude and period. In this paper, we determine the magnitude of an impulse force required to stop the oscillations of a simple harmonic oscillator of a mass spring system. The magnitude of the impulse force is obtained as the product of the mass, frequency and amplitude of the oscillations. Depending on the direction and time instant this impulse force is applied, the resulting amplitude of the oscillations can attain a minimum value of zero or a maximum value of double the initial amplitude. We propose the optimal time instants and direction to apply the impulse force in order to stop the oscillations.

MSC:

34A37 Ordinary differential equations with impulses
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
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