# 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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