Explanation
Here effective acceleration due to gravity = (g – a).
Two springs each of spring constant k1 in parallel, give equivalent spring constant of 2 k1 and this is in series with spring of constant k2, so equivalent spring constant,
x = a sin ωt and y = a sin (ωt + π/2) = a cos ωt,
so x2 + y2 = a2 (sin2ωt + cos2ωt) = a2;
It is an equation of a circle.
Amplitude resonance takes place at a frequency of external force which is less than the frequency of undamped natural vibrations. Velocity resonance takes place (i.e. max. energy) when frequency of external periodic force is equal to natural frequency of undamped vibrations.
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