Question

A particle has shifted along some trajectory in the plane xy from point 1 whose radius vector r1 = i +2j to point 2

Answer 1

It's from Irodov
so see the attachment for the answer

Answer 2

The potential energy of a particle executing SHM varies sinusoidally with frequency f. Potential energy reaches its maximum value to the maximum in T/2 time, while the oscillation takes T time.

So, the frequency of the oscillation is the half of frequency of the potential energy. i.e. f/2 as f α 1/T. or, I/T = fp/ fu = Tu/Tp = Tu/ Tp = (T/2)/ T = ½.