Just hanging around- part 1

Classical Mechanics Level 3

If the time period of simple harmonic motion of the rectangular block can be represented as \[T=2\pi \sqrt{\frac{am}{bk}}\] for coprime positive integers \(a,b\).

Find \(\sqrt{a^2+b^2}\) up to two decimal places.

Details and Assumptions

Pulley is smooth and massless, and the strings are light and inextensible.
Gravity is present.
The crooked lines in the figure represents springs of spring constant \(k\) and \(2k\) as shown.

-Take the amplitude of oscillations to be very small.

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