Angular Frequency

A series LCR circuit containing 5.0 H inductor, 80 mu F capacitor and 40 Omega resistor is connected to 230 V variable frequency ac source. The angular frequencies of the source at which power transfered to circuit is half the power at resonant angular frequency are likely to be.

Two equal masses are connected by a spring satisfying Hook's law and are placed on a frictionless table. The spring is elongated a little and allowed to go. Let the angular frequency of oscillations be omega . Noe one of the masses is stopped. The square of the new angular frequency is :

A series LCR circuit containing a resistance of 120 Omega has angular resonance frequency 4 xx 10^(5) "rads"^(-1) . At resonance the voltages across resistance and inductance are 60 V and 40 V respectively. (a) The value of L and C are 0.2 mH, 1/32 muF (b) If angular frequency is changed to 8xx10^(5) "rad"//s , the current lags the voltage by 45^(@) (c) If angular frequency is charged to 6xx10^(5) "rad"//s , the current lags the voltage by 45^(@)

In R-L-C series circuit, we have same current at angular frequencies omega_(1) and omega_(2) . The resonant frequency of circuit is

Two discs of moments of inertia I_1 and I_2 about their respective axes, rotating with angular frequencies, omega_1 and omega_2 respectively, are brought into contact face to face with their axes of rotation coincident. The angular frequency of the composite disc will be A .

The number of harmonic components in the oscillations are represented by, y=4cos^(2)(2 tsin4t) . What are their corresponding angular frequencies?