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

A student writes four different expressions for the displacement `y` i

1.	A student writes four different expressions for the displacement `y` in a periodic motion . Which of the following can be correct?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» Correct Answer - D 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)`.

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

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