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 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 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.

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.

The transvers displacement of a string (clamped at its both ends) is given by y(x,t) = 0.06 sin ((2pi)/(3)s) cos (120 pit) Where x and y are in m and t in s. The length of the string 1.5 m and its mass is 3.0 xx 10^(-2) kg. Does the function represent a travelling wave or a stationary wave ?

The transvers displacement of a string (clamped at its both ends) is given by y(x,t) = 0.06 sin ((2pi)/(3)s) cos (120 pit) Where x and y are in m and t in s. The length of the string 1.5 m and its mass is 3.0 xx 10^(-2) kg. Interpret the wave as a superposition of two waves travelling in opposite directions. What is the wavelength, frequency, and speed of each wave ?

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