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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