# 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 $${a^2+b^2}$$

Details

• 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

×