Out of the following functions representing motion of a particle which represent SHM? (a) y= sin omega t- cos omega t (b) y= sin^(2) omega t (c ) y= 5cos ((3pi)/(4)-3 omega t) (d) y= 1+ omega t+ omega^(2) t^(2)
The following equations represent transverse waves : z_(1) = A cos(kx - omegat) , z_(2) = A cos (kx + omegat) , z_(3) = A cos (ky - omegat) Identify the combination (s) of the waves which will produce (i) standing wave(s), (ii) a wave travelling in the direction making an angle of 45^(@) with the positive x and positive y axes. In each case, find the positions at which the resultant is always zero.
Which of the following functions of time represent (a) simple harmonic, (b) periodic but not simple harmonic, and (c) non-periodic motion? Give period for each case of periodic motion ( omega is any positive constant): (a) sinomegat-cosomegat (b) sin^(3)omegat (c) 3cos(pi//4-2omegat) (d) cosomegat+cos3omegat+cos5omegat (e) exp(-omega^(2)t^(2)) (f) 1+omegat+omega^(2)t^(2)
Find the derivative of the following functions with respect to x sin [cos(x^(2))]
Which of the following functions of time represent (a) periodic and (b) non-periodic motion? Give the period for each case of periodic motion [ omega is any positive constant]. (i) sinomegat+cosomegat (ii) sinomegat+cos2omegat+sin4omegat (iii) e^(-omegat) (iv) log(omegat)
Find the resulting amplitude A' and the phase of the vibrations delta S = Acos(omegat) + A/2 cos (omegat + pi/2) + A/2 cos (omega t + pi) + A/8 cos (omegat + (3pi)/(2)) = A' cos (omega t + delta)
The function sin^(2) (omegat) represents.
Which of the following functions of time represent (a) simple harmonic motion and (b) periodic but not simple harmonic? Give the period for each case. (1) sinomegat-cosomegat (2) sin^(2)omegat
Find (i) int cos^(2)x,dx (ii) int sin (2x)cos (3x)dx , (iii) int sin^(3)x dx.
Integrate the following functions : e^(x)((2+sin2x)/(1+cos2x))
