# Optics or Classical Mechanics

Mayank and Akul had their birthdays last Friday. They got 2 spotlights, a detector and a spring in their birthday presents. They thought of doing something crazy.

Akul welded the spotlights at the ends of the spring and Mayank took the detector and ran around in a circle of very large radius with its centre coinciding with the centre of spring as shown.

At $$t=0$$, spring was in its $$relaxed$$ $$state$$, Mayank was at $$\theta =0$$ and Akul gave the spring an impulse, such that it starts oscillating. Mayank changed his position with time in such a way that he $$ALWAYS$$ detected a $$first$$ order $$maxima$$.

It is known that:-

1) Mayank moved from $$\theta \epsilon \left[ 0,\frac { \pi }{ 4 } \right]$$

2) The mass of spotlights is $$1kg$$ and spring constant is $$1N/m$$.

3) Always means at each and every instant of time.

4) Akul gives impulse such that the spring expands at t=0 i.e. outward impulse.

Find Mayank's angular position as a function of time. Give your answer(in degrees) as his position at $$t=1$$ second.

Wanna have more fun with Mayank and Akul. This question is a part of the set Mayank and Akul

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