Rule out or accept the following formula for displacement y of particle undergoing periodic motion on the basis of dimentional arguments :
(i) `a sin 2pi t"/"T`
(ii) `a cos vt`
(iii) `a sin (omegat -kx)`
where a= maximum displacement of the particle T= time period of motion, t= time interval, v= speed of particle, `omega`= Angular speed of particle, k= displacement constant.

Explanation

To determine whether the given formulas for displacement \( y \) of a particle undergoing periodic motion are dimensionally correct, we will analyze each formula step by step.

### Given Formulas:
1. \( y = a \sin \left( \frac{2\pi t}{T} \right) \)
2. \( y = a \cos(vt) \)
3. \( y = a \sin(\omega t - kx) \)

Where:
...