A book with many printing errors contains four different formulae for the displacement y of a particle undergoing a certain periodic motion : `y=a sin vt` (a = maximum displacement of the particle, v= speed of the particle, T = time-period of motion). Rule out the wrong formula on dimensional grounds.

The displacement of a particle in simple harmonic motion in one time period is

A book with many printing errors contains four different forumlae for the displacement y of a particle undergoing a certain periodic motion : (i) y = a sin (2pi t)/(T) (ii) y = a sin upsilon t (iii) y = (a)/(T) sin (t)/(a) (iv) y= (a)/(sqrt2)[sin(2pi t)/(T) + cos (2pi t)/(T)] Here, a is maximum displacement of particle, upsilon is speed of particle, T is time period of motion. Rule out the wrong forumlae on dimensinal grounds.

The displacement of a particle is represented by the equation y=sin^(3)omegat. The motion is

The displacement of a particle executing S.H.M. is given by, y = 0.20 sin (100 t) cm. The maximum speed of the particle is

The displacement of a particle is repersented by the equation y=sin^(3)omegat . The motion is