The displacement vector of a partical of mass m is given by
`vecr(t) = hat iA cos omega t + hatj B sin omegat`.
Show that `vecF = - momega^2vecr`

The displacement vector of a partical of mass m is given by vecr(t) = hat iA cos omega t + hatj B sin omegat . Show that the trajectory is an ellipse.

The displacement of an elastic wave is given by the function y=3sin omegat+4 cos omegat where y is in cm and t is in second. Calculate the resultant amplitude.

The displacemnt of a particle inS.H.M. may be given by y = r sin (omegat + phi_0) . Show that if the time t is increased by (2pi)/omega the value of y remains unchanged.

The velocity of a body of mass 2 kg as a function of t is given by vec v (t) = 2t hat i + t^2 hatj . Find the momentum and the force acting on it, at time t = 2s.

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

Out of the followingg functions representing motion of a particle which represent SHM? y=sin omegat-cos omega t y=sin^2 omega t y=5cos((3pi)/4 - 3 omega t) y=1 + omega t+ omega^2 t^2 .

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 motion of a particle executing simple harmonic motion is described by the displacement function, x(t) = A cos (omegat + phi) . If the initial (t = 0) position of the particle is 1 cm and its initial velocity is omega cm//s , what are its amplitude and initial phase angle ? The angular frequency of the particle is pi s^-1 s If instead of the cosine function, we choose the sine function to describe the SHM : x= B sin (omegat+alpha) , what are the amplitude and initial phase of the particle with the above initial conditions.

Vectors vec a , vec b , vec c and vec d are given by vec a= hat i+ hat j+ hat k , vec b= 2 hat i+ 3 hat j , vec c= 3 hat i+ 5 hat j- 2 hat k and vec d= - hat j+ hat k . Show that the vectors vec b- vec a and vec d- vec c are parallel and find the ratio of their lengths.