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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