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physics
oscillations mechanical waves

Questions and Answers of Oscillations Mechanical Waves

An oscillating circuit consists of an inductance coil L and a capacitor with capacitance C. The resistance of the coil and the lead wires is negligible. The coil is placed in a permanent magnetic
The free damped oscillations are maintained in a circuit, such that the voltage across the capacitor varies as V = V me–βt cos w Find the moments of time when the modulus of the voltage across
A certain oscillating circuit consists of a capacitor with capacitance C, a coil with inductance L and active resistance and a switch. When the switch was disconnected, the capacitor was charged;
A circuit with capacitance C and inductance L generates free damped oscillations with current varying with time as I = I me–βt sin wt. Find the voltage across the capacitor as a function of
An oscillating circuit consists of a capacitor with capacitance C = 4.0μF and a coil with inductance L = 2.0 mH and active resistance R = l0 Ω. Find the ratio of the energy of the coil's
An oscillating circuit consists of two coils connected in series whose inductances are L1 and L2, active resistances are R1 and R2, and mutual inductance is negligible. These coils are to be replaced
How soon does the current amplitude in an oscillating circuit with quality factor Q = 5000 decrease η = 2.0 times if the oscillation frequency is v = 2.2 MHz?
An oscillating circuit consists of capacities C = l0μF, inductance L = 25 mH, and active resistance R 1.0Ω. How many oscillation periods does it take for the current amplitude to decrease
How much (in per cent) does the free oscillation frequency w of a circuit with quality factor Q = 5.0 differ from the natural oscillation frequency wo of that circuit?
In a circuit shown in Fig. 4.29 the battery emf is equal to ε = 2.0 V, its internal resistance is r = 9.0Ω, the capacitance of the capacitor is C = l0μF, the coil inductance is L =
Damped oscillations are induced in a circuit whose quality factor is Q = 50 and natural oscillation frequency is v0 = 5.5 kHz. How soon will the energy stored in the circuit decrease η = 2.0
An oscillating circuit incorporates a leaking capacitor. Its capacitance is equal to C and active resistance to R. The coil inductance is L. The resistance of the coil and the wires is negligible.
Find the quality factor of a circuit with capacitance C = 2.0μF and inductance L = 5.0mH if the maintenance of un-damped oscillations in the circuit with the voltage amplitude across the
What mean power should be fed to an oscillating circuit with active resistance R = 0.45Ω to maintain un-damped harmonic oscillations with current amplitude Im = 30 mA?
An oscillating circuit consists of a capacitor with capacitance C = 1.2nF and a coil with inductance L = 6.0μH and active resistance R = 0.50Ω. What mean power should be fed to the circuit
Find the damped oscillation frequency of the circuit shown in Fig. 4.30. The capacitance C, inductance L, and active resistance R are supposed to be known. Find how must C, L and R be interrelated to
There are two oscillating circuits (Fig. 4.31) with capacitors of equal capacitances. How must inductances and active resistances of the coils be interrelated for the frequencies and damping of free
A circuit consists of a capacitor with capacitance C and a coil of inductance L connected in series, as well as a switch and a resistance equal to the critical value for this circuit. With the switch
A coil with active resistance R and inductance L was connected at the moment t = 0 to a source of voltage V = Vm cos cot. Find the current in the coil as a function of time t.
A circuit consisting of a capacitor with capacitance C and a resistance R connected in series was connected at the moment t = 0 to a source of ac voltage V = Vm cos cot. Find the current in the
A long one-layer solenoid tightly wound of wire with resistivity p has n turns per unit length. The thickness of the wire insulation is negligible. The cross-sectional radius of the solenoid is equal
A circuit consisting of a capacitor and an active resistance R= 110Ω connected in series is fed an alternating voltage with amplitude Vm = 110V. In this case the amplitude of steady-state
Fig. 4.32 illustrates the simplest ripple filter. A voltage V = V o (l + cos wt) is fed to the left input. Find:(a) The output voltage V' (t);(b) The magnitude of the product R at which the output
Draw the approximate voltage vector diagrams in the electric circuits shown in Fig. 4.33 a, b. The external voltage V is assumed to be alternating harmonically with frequency w.
A series circuit consisting of a capacitor with capacitance C = 22μF and a coil with active resistance R = 20Ω and inductance L = 0.35H is connected to a source of alternating voltage with
A series circuit consisting of a capacitor with capacitance C, a resistance R, and a coil with inductance L and negligible active resistance is connected to an oscillator whose frequency can be
An alternating voltage with frequency w = 314 s-and amplitude Vm = 180 V is fed to a series circuit consisting of a capacitor and a coil with active resistance R = 40Ω and inductance L = 0.36 H.
A capacitor with capacitance C whose interelectrode space is filled up with poorly conducting medium with active resistance R is connected to a source of alternating voltage V = Vm cos cot. Find the
An oscillating circuit consists of a capacitor of capacitance C and a solenoid with inductance L1. The solenoid is inductively connected with a short-circuited coil having an inductance L2 and a
Find the quality factor of an oscillating circuit connected in series to a source of alternating emf if at resonance the voltage across the capacitor is n times that of the source.
An oscillating circuit consisting of a coil and a capacitor connected in series is fed an" alternating emf, with coil inductance being chosen to provide the maximum current in the circuit. Find the
A series circuit consisting of a capacitor and a coil with active resistance is connected to a source of harmonic voltage whose frequency can be varied, keeping the voltage amplitude constant. At
Demonstrate that at low damping the quality factor Q of a circuit maintaining forced oscillations is approximately equal to wo/∆w, where wo is the natural oscillation frequency, ∆w is the
A circuit consisting of a capacitor and a coil connected in series is fed two alternating voltages of equal amplitudes but different frequencies. The frequency of one voltage is equal to the natural
It takes t o hours for a direct current I o to charge a storage battery. How long will it take to charge such a battery from the mains using a half-wave rectifier, if the effective current value is
Find the effective value of current if its mean value is I and its time dependence is(a) Shown in Fig. 4.34;(b) I ~, | sin wt |
A solenoid with inductance L = 7 mH and active resistance R = 44Ω is first connected to a source of direct voltage Vo and then to a source of sinusoidal voltage with effective value V = Vo. At
A coil with inductive resistance XL = 30Ω and impedance Z = 50Ω is connected to the mains with effective voltage value V = 100 V. Find the phase difference between the current and the
A coil with inductance L = 0.70H and active resistance r = 20Ω is connected in series with an inductance-free resistance R. An alternating voltage with effective value V = 220 V and frequency w
A circuit consisting of a capacitor and a coil in series is connected to the mains. Varying the capacitance of the capacitor, the heat power generated in the coil was increased n = 1.7 times. How
A source of sinusoidal emf with constant voltage is connected in series with an oscillating circuit with quality factor Q = 100. At a certain frequency of the external voltage the heat power
A series circuit consisting of an inductance-free resistance R = 0.16kΩ and a coil with active resistance is coroneted to the mains with effective voltage V = 220 V. Find the heat power
A coil and an inductance-free resistance R = 25Ω are connected in parallel to the ac mains. Find the heat power generated in the coil provided a current I = 0.90 A is drawn from the mains. The
An alternating current of frequency w = 314 s-1 is fed to a circuit consisting of a capacitor of capacitance C = 73μF and an active resistance R = 100Ω connected in parallel. Find the
Draw the approximate vector diagrams of currents in the circuits shown in Fig. 4.35. The voltage applied across the points A and B is assumed to be sinusoidal; the parameters of each circuit are so
A capacitor with capacitance C = 1.0μF and a coil with active resistance R = 0.10Ω and inductance L = 1.0mH are connected in parallel to a source of sinusoidal voltage V = 31 V. Find: (a)
A capacitor with capacitance C and a coil with active resistance R and inductance L are connected in parallel to a source of sinusoidal voltage of frequency w. Find the phase difference between the
A circuit consists of a capacitor with capacitance C and a coil with active resistance R and inductance L connected in parallel. Find the impedance of the circuit, at frequency (o of alternating
A ring of thin wire with active resistance R and inductance L rotates with constant angular velocity w in the external uniform magnetic field perpendicular to the rotation axis. In the process, the
A wooden core (Fig. 4.36) supports two coils: coil 1 with inductance L1 and short-circuited coil 2 with active resistance R and inductance L 2. The mutual inductance of the coils depends the distance
An electromagnetic wave of frequency w = 3.0 MHz passes from vacuum into a non-magnetic medium with permittivity e = 4.0. Find the increment of its wavelength.
A plane electromagnetic wave falls at right angles to the surface of a plane-parallel plate of thickness l. The plate is made of non-magnetic substance whose permittivity decreases exponentially from
A plane electromagnetic wave of frequency v = 10 MHz propagates in a poorly conducting medium with conductivity σ = 10 mS/m and permittivity ε = 9. Find the ratio of amplitudes of
A plane electromagnetic wave E = Em cos (wt – kr) propagates in vacuum. Assuming the vectors E m and k to be known, find the vector H as a function of time t at the point with radius vector r = 0.
A plane electromagnetic wave E = Em cos (wt – kr), where Em = Emey, k = kex, ex, ey are the unit vectors of the x, y axes, propagates in vacuum. Find the vector H at the point with radius vector r
A plane electromagnetic wave E = Em cos (w €“ kx) propagating in vacuum induces the emf ε ind in a square frame with side l. The orientation of the frame is shown in Fig. 4.37. Find
Proceeding from Maxwell's equations show that in the case of a plane electromagnetic wave (Fig. 4.38) propagating in vacuum the following relations hold:
Find the mean Poynting vector (S) of a plane electromagnetic wave E = Em cos (wt – kr) if the wave propagates in vacuum.
A plane harmonic electromagnetic wave with plane polarization propagates in vacuum. The electric component of the wave has a strength amplitude Em = 50 mV/m the frequency is v = 100 MHz. Find: (a)
A ball of radius R = 50 cm is located in a non-magnetic medium with permittivity e = 5.0. In that medium a plane electromagnetic wave propagates, the strength amplitude of whose electric component is
A standing electromagnetic wave with electric component E = Em cos kx ∙ cos wt is sustained along the x axis in vacuum. Find the magnetic component of the wave B (x, t). Draw the approximate
A standing electromagnetic wave E = Em cos kx ∙ cos (or is sustained along the x axis in vacuum. Find the projection of the Poynting vector on the x axis Sx (x, t) and the mean value of that
A parallel-plate air capacitor whose electrodes are shaped as discs of radius R = 6.0 cm is connected to a source of an alternating sinusoidal voltage with frequency w = 1000 s-1. Find the ratio of
An alternating sinusoidal current of frequency w = 1000 s-1 flows in the winding of a straight solenoid whose cross-sectional radius is equal to R = 6.0 cm. Find the ratio of peak values of electric
A parallel-plate capacity whose electrodes are shaped as round discs is charged slowly. Demonstrate that the flux of the Poynting vector across the capacitor's lateral surface is equal to the
A current I flows along a straight conductor with round cross-section. Find the flux of the Poynting vector across the lateral surface of the conductor's segment with resistance R.
Non-relativistic protons accelerated by a potential difference U form a round beam with current I. Find the magnitude and direction of the Poynting vector outside the beam at a distance r from its
A current flowing in the winding of a long straight solenoid is increased at a sufficiently slow rate. Demonstrate that the rate at which the energy of the magnetic field in the solenoid increases is
Fig. 4.39 illustrates a segment of a double line carrying direct current whose direction is indicated by the arrows. Taking into account that the potential φ2 > φ1, and making use of the
The energy is transferred from a source of constant voltage V to a consumer by means of a long straight coaxial cable with negligible active resistance. The consumed current is I. Find the energy
A source of ac voltage V = Vo cos cot delivers energy to a consumer by means of a long straight coaxial cable with negligible active resistance. The current in the circuit varies as I = Io cos wt =
Demonstrate that at the boundary between two media the normal components of the Poynting vector are continuous, i.e. Sin = S8n.
Demonstrate that a closed system of charged non-relativistic particles with identical specific Surges emits no dipole radiation.
Find the mean radiation power of an electron performing harmonic oscillations with amplitude a = 0.10 nm and frequency w = 6.5 ∙ 1014 s -1.
Find the radiation power developed by a non-relativistic particle with charge e and mass m, moving along a circular orbit of radius R in the field of a stationary point charge q.
A particle with charge e and mass m flies with non-relativistic velocity v at a distance b past a stationary particle with charge q neglecting the bending of the trajectory of the moving particle,
A non-relativistic proton enters a half-space along the normal to the transverse uniform magnetic field whose induction equals B = 1.0 T. Find the ratio of the energy lost by the proton due to
A non-relativistic charged particle moves in a transverse uniform magnetic field with induction B. Find the time dependence of the particle's kinetic energy diminishing due to radiation. How soon
A charged particle moves along the y axis according to the law y = a cos wt, and the point of observation P is located on the x axis at a distance l from the particle (1 >> a). Find the ratio of
A charged particle moves uniformly with velocity v along a circle of radius R in the plane xy (Fig. 4.40). An observer is located on the x axis at a point P which is removed from the centre of the
An electromagnetic wave emitted by an elementary dipole propagates in vacuum so that in the far field zone the mean value of the energy flow density is equal to so at the point removed from the
The mean power radiated by an elementary dipole is equal to Po. Find the mean space density of energy of the electromagnetic field in vacuum in the far field zone at the point removed from the dipole
An electric dipole whose modulus is constant and whose moment is equal to p rotates with constant angular velocity w about the axis drawn at right angles to the axis of the dipole and passing through
A free electron is located in the field of a plane electromagnetic wave. Neglecting the magnetic component of the wave disturbing its motion, find the ratio of the mean energy radiated by the
A plane electromagnetic wave with frequency w falls upon an elastically bonded electron whose natural frequency equals wo. Neglecting the damping of oscillations, find the ratio of the mean energy
Assuming a particle to have the form of a ball and to absorb all incident light find the radius of a particle for which its gravitational attraction to the Sun is counterbalanced by the force that
A point oscillates along the x axis according to the law x = a cos (wt = π/4). Draw the approximate plots (a) Of displacement x, velocity projection Vx, and acceleration projection Wx as
A point moves along the x axis according to the law x = a sin2 (wt – π/4). Find: (a) The amplitude and period el oscillations; draw the plot x (t); (b) The velocity projection vx as a
A particle performs harmonic oscillations along the x axis about the equilibrium position x = 0. The oscillation frequency is w = 4.00 s-1. At a certain moment of time the particle has a coordinate
Find the angular frequency and the amplitude of harmonic oscillations of a particle if at distances x 1 and x2 from the equilibrium position its velocity equals V1 and V2 respectively.
A point performs harmonic oscillations along a straight line with a period T = 0.60 s and an amplitude a = 10.0 cm. Find the mean velocity of the point averaged over the time interval during which it
At the moment t = 0 a point starts oscillating along the x axis according to the law x = a sin (or. Find: (a) The mean value of its velocity vector projection (vx); (b) The modulus of the mean
A particle moves along the x axis according to the law x = a cos wt. Find the distance that the particle covers during the time interval from t = 0 to t.
At the moment t = 0 a particle starts moving along the x axis so that its velocity projection varies as vx = 35 cos πt cm/s, where t is expressed in seconds. Find the distance that this particle
A particle performs harmonic oscillations along the x axis according to the law x = a cos (or. Assuming the probability P of the particle to fall within an interval from – a to + a to be equal to
Using graphical means, find an amplitude a of oscillations resulting from the superposition of the following oscillations of the same direction: (a) x1 = 3.0 cos (wt + π/3), x2 = 8.0sin (wt +
A point participates simultaneously in two harmonic oscillations of the same direction: x1 = a cos wt and x2 = a cos 2wt. Find the maximum velocity of the point.
The superposition of two harmonic oscillations of the same direction results in the oscillation of a point according to the law x = a cos 2.1t cos 50.0t, where t is expressed in seconds. Find the
A point A oscillates according to a certain harmonic law in the reference frame K' which in its turn performs harmonic oscillations relative to the reference frame K. Both oscillations occur along
A point moves in the plane xy according to the law x = a sin wt, y = b cos cot, where a, b, and co are positive constants. Find: (a) The trajectory equation y (x) of the point and the direction of

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