Without a compensating energy-loss mechanism provided by \ beta, the oscillation amplitude grows exponentially . ( This phenomenon is called "'parametric excitation "', "'parametric resonance "'or "'parametric pumping "'. ) However, if the initial amplitude is zero, it will remain so; this distinguishes it from the non-parametric resonance of driven simple harmonic oscillators, in which the amplitude grows linearly in time regardless of the initial state.
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