A student writes four different expressions for the displacement `y` in a periodic motion . Which of the following can be correct?

Options

A. ` y = a T sin ( 2 pi t)/(T)`
B. ` y = a sin V t`
C. ` y = (a)/( T) sin ( t)/(a)`
D. ` y = (a)/ (sqrt(2))[ sin (2pi t)/(T) + cos (2pi t)/(T)]`

Answer

D

Explanation

Since `LHS` is displacement , so `RHS` should have dimensions of displacement . In `(a) , aT` does not have the dimensions of displacement . Also the argument of a trigonometric function should be dimensionless . In `(b)` , argument is not dimensionless and in `( c) , a//T` does not have the dimensions of displacement . Hence , the correct choice is `(d)`.