Question

A book with printing error contains four different formulae for displacement. Choose the correct formula/formulae

(a) y = a sin 2π/T t

(b) y = a sin vt

(c) y = a/T sin(t/a)

(d) y = a/T(sin 2π/T t + cos 2π/T t)

Answer 1

The argument of sine and cosine function must be dimensionless so (a) is the probable correct formula. Since

 

= [T⁰] is dimensionless.

(b) y = a sin vt, ∴ [vt] = [L] is dimensional so this equation is incorrect.

(c) y = a/t sin (t/a), ∴ [t/a] is dimensional so this is incorrect.

(d) y = a/t(sin 2π/T t + cos 2πt/T) : Though 2πt/T dimensionless a/T does not have dimensions of displacement so this is also incorrect.