Find the limiting values of amplitude of a force damped oscillator, when (i) `omega_d ltlt omega_0` and (ii) `omega_d gtgt omega_0`.

Evaluate: (i) omega (ii) omega^(2) (iii) omega^(3)

Find the value of w : -2/3 = 6/w

Demonstrate thatat low damping the quality factor Q of a circuit maintaining forced oscillations is approximately equal to omega_(0)//Delta omega , where omega_(0) is the natural oscillation frequency , Delta omega is the width of the resonance curve I(omega) at the " height " which is sqrt(2) times less than the resonance current amplitude.

The equation of displacement of a harmonic oscillator is x = 3sin omega t +4 cos omega t amplitude is

Derive the three equation of rotational motion (i) omega = omega_(0) + at (ii) theta = omega_(0)t + 1/2alpha t^(2) (iii) omega^(2) = omega_(0)^(2) + 2alpha theta Under constant angular acceleration. Here symbols have usual meaning.

Find the value of ( i ) (omega)^12 ( ii ) ( omega )^81

Find the rms value of current i=I_(m)sin omegat from (i) t=0 "to" t=(pi)/(omega) (ii) t=(pi)/(2omega) "to" t=(3pi)/(2omega)

Which of the following cannot be valid assignmentof probabilities for outcomes of sample space S={omega_(1),omega_(2),omega_(3),omega_(4),omega_(5),omega_(6),omega_(7)} ? Assignement omega_(1),omega_(2),omega_(3),omega_(4),omega_(5),omega_(6),omega^(7) a. 0.1,0.01,0.05,0.03,0.01,0.3,0.6 b. 1/7,1/7,1/7,1/7,1/7,1/7,1/7 c. 0.1,0.2,0.3,0.4,0.5,0.6,0.7 d. -0.1,0.2,0.3,0.4,-0.2,0.1,0.3 e. 1/14,2/14,3/14,4/14,5/14,6/14,15/14