Infinite oscillating springs

Classical Mechanics Level pending

There is a system of infinite pulleys and springs as shown in the figure above. Spring constants follows a geometric progression, \(K, 2K, 4K, 8K, \ldots\). All the pulleys are massless and frictionless. Find the time period of oscillation.

Take the mass of the block to be \(m\). If the answer is of the form \( T =2\pi \sqrt{Bm/K} \), where \(B\) is a natural number, submit your answer as \(B\).

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