Just hanging around , Medium part2

If the time period of SHM of rectangular block can be represented as T=2πambkT=2\pi \sqrt{\frac{am}{bk}}. Find a2+b2{a^2+b^2}

Details

  • The pulley is smooth with mass mm, 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.
  • aa is of the form c+d\sqrt c +d where cc is a square free integer. And bb is of the form efe\sqrt f where ff 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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