Just hanging around- part 1

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

Find a2+b2\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 kk and 2k2k as shown.

-Take the amplitude of oscillations to be very small.


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