# 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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