Irodov – Problems in General Physics

(b) the frequency co of the force F at which (P) is maximum; what

is (P),,„„ equal to?

4.92. An external harmonic force F whose frequency can be varied,

with amplitude maintained constant, acts in a vertical direction on

a ball suspended by a weightless spring. The damping coefficient is

times less than the natural oscillation frequency coo of the ball.

How much, in per cent, does the mean power (P) developed by the

force F at the frequency of displacement resonance differ from the

maximum mean power (P)max? Averaging is performed over one

oscillation period.

4.93. A uniform horizontal disc fixed at its centre to an elastic

vertical rod performs forced torsional oscillations due to the moment

of forces N, = N,„ cos wt. The oscillations obey the law cp =

cp n, cos (cot — cc). Find:

(a) the work performed by friction forces acting on the disc during

one oscillation period;

(b) the quality factor of the given oscillator if the moment of

inertia of the disc relative to the axis is equal to I.

4.2. Electric Oscillations

• Damped oscillation in a circuit

where

q me-6,t cos (cot-1-a),

04 — 132 ,^ (4- -VW 13= 2L

1

(4.2a)

• Logarithmic damping decrement and quality factor Q of a circuit are
  defined by Eqs. (4.1d). When damping is low:

X = nil 1 7 --C L - , Q= 77 V —C- • (4.2b)

1.. r

• Steady-state forced oscillation in a circuit with a voltage V = Vm cos cot
  connected in series:
  / = /7)., cos (cot — (p),^ (4.2c)
  where

Vm

1/R 2 + (coL —

COC \

2

Im R

tan cp-

(4.2d)

wL —

1 0

coC

R In7MC

Axis

of current

Fig. 4.26.

The corresponding vector diagram for voltages is shown in Fig. 4.26.

• Power generated in an ac circuit:

P = VI cos p, (^) (4.2e)
where V and I are the effective values of voltage and current:
V = V„/ VT, 1= in,117-1. (4.2f)