Just hanging around , Medium part2

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


  • 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

  • Try its different variants - Easier and hardest


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