A book with printing error contains four different formulae for displacement. Choose the correct formula/formulae
(a) y = a sin `(2pi)/(T)t` (b) y = a sin vt (c) y = `a/T sin (t/a)`
(d) y = `a/T (sin (2pi)/(T) t + cos (2pi)/(T) t)`

Explanation

The argument of sine and cosine function must be dimensionaless so (a) is the probable correct formula. Since
(a) y = a sin `((2pi)/(T)t), :. [(2pit)/(T)] = [T^(0)]` is dimensionless.
(b) y = a sin vt, `:. [vt] = [T]` is dimensional so this equation is incorrect.
(c) y = `a/t sin (t/a), :. [t/a]` is dimensional so this is incorrect.
(b) y = `a/t (sin ""(2pi)/(T) t + cos"" (2pit)/(T))` , Though `(2pit)/(T)` dimensionless `a/T` does not have dimension of displacement so this is also incorrect.