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in Physics by (24.2k points)

Choose the correct formulae for the displacement (y) of a particle executing periodic motion?

(i) y = r sin (2π/T)t

(ii) y = r sin vt

(iii) y = r sin (2π/t)t 

(iv) y = r sin (2π/v)t

where T, r, v and t stand for time period, amplitude, velocity and time respectively.

1 Answer

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The argument of a trigonometric function (usually called angle) is a dimensionless quantity. Only in first expression, the angle. i.e., 2π/T x t is dimensionless. In other equations, the factor vt, (2π/t)t and (2π/v)t have dimensions of [L], [L-1 T2] respectively. Hence, the displacement of the particle is given only by the first expression, i.e.,[y = sin 2π/T x t].

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