Out of the formulae y =a sin `2pi t//T` and y = a sin `upsilon t` for the displacement y of particle undergoing a periodic motion, rule out the wrong formula on the basis of dimensions. Symbols have standard meaning.

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 varies with time according to the relation y=a sin omega t +b cos omega t .

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.

Rule out or accept the following formula for displacement y of particle undergoing periodic motion on the basis of dimentional arguments : (i) a sin 2pi t"/"T (ii) a cos vt (iii) a sin (omegat -kx) where a= maximum displacement of the particle T= time period of motion, t= time interval, v= speed of particle, omega = Angular speed of particle, k= displacement constant.

The displacement of a particle excuting periodic motion is given by y=4cos^(2)(t//2)sin(1000t) . Find the independent constituent SHM's.

The displacement of a represnted by the equation y = sin^(2) omega t the motion is

The displacement y of a particle periodic motion is given by y = 4 cos ((1)/(2) t) sin (1000 t) This expression may be considered as a result of the superposition of