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 instantaneous acceleration of a particle executign S.H.M. Given by y = a sin omegat , is

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 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 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

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

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 ?

For a given a.c., I = I_0 sin omegat , show that the average power dissipated in a resistor R over a complete cycle is 1/2 I_0^2R .