If the time period of SHM of rectangular block can be represented as \(T=2\pi \sqrt{\frac{am}{bk}}\). Find \({a^2+b^2}\)

**Details**

- The pulley is smooth with mass \(m\), the strings are massless and inextensible.
- The two springs are in phase.
- The pulley system is in a uniform gravitational field.
- Zig-zag lines in fig represents spring of spring constant k and 2k as shown.
- \(a\) is of the form \(\sqrt c +d\) where \(c\) is a square free integer. And \(b\) is of the form \(e\sqrt f\) where \(f\) is square free integer.
The pulley and the block oscillate in phase with the same frequency

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