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