A book with many printing errors contains four different formulas 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 formulas on dimensional grounds.

A book with many printing errors contains four different formulas for the displacement y of a particle undergoing a certain periodic motion :- y=a sin 2pi t//T (a = maximum displacement of the particle, v = speed of the particle. T= time-period of motion). Rule out the wrong formulas on dimensional grounds.

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

A book with many printing errors contains four different formulas for the displacement y of a particle undergoing a certain periodic motion :- y=(asqrt2)(sin2pit//T+cos2pit//T) (a = maximum displacement of the particle, v = speed of the particle. T= time-period of motion). Rule out the wrong formulas on dimensional grounds.

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

The displacement of a progressive wave is represented by y = A sin (omegat - kx) , where x is distance and t is time. Write the dimensional formula of omega

The displacement of a progressive wave is represented by y = A sin (omegat - kx) , where x is distance and t is time. Write the dimensional formula of k

Show that the motion of a particle represented by y = sin omega t - cos omegat is simple harmonic with a period of 2pi//omega .