3.4 Universality of a Computer Model and Equivalent Physical …
127
Fig. 3.30 Torsion spring
oscillator
To describe real vibrational dynamical systems, some physical model is used,
which is called a linear or harmonic oscillator. This model introduces some basic
assumptions.
If the oscillator is once removed from the state of equilibrium, then a restoring
force will arise in such a system, which will tend to return the oscillator back to
the equilibrium position. The restoring force in magnitude is directly proportional to
the displacement and directed against the displacement. The physical quantities that
describe the oscillations of the oscillator change with time according to the harmonic
law of cosine or sine.
However, there are quite a lot of oscillatory systems to which the linear oscillator
model is applicable:
(a) spring pendulum—a load suspended on an elastic spring, which obeys Hooke’s
law at small displacements;
(b) the mathematical and physical pendulums that make small deviations from the
vertical in the gravitational field;
(c) an electric oscillatory circuit, consisting of a precharged capacitor, coil, and
resistor, which are connected in series in a circuit;
(d) torsion spring oscillator.
Let us consider it in more detail; see Fig. 3.30.
The oscillator consists of a disk (or rotor), which can rotate relative to a fixed axis
perpendicular to the plane in which the rotor is located. The rotor is engaged with a
weightless coil spring at one of its ends. The other end of the spring is rigidly fixed.
When the disk is rotated by a certain angle relative to point 0 (equilibrium position),
the spring, elastically deformed, twists, and the rotor stops in the extreme position.
Then the spring unwinds, returning the disk to the equilibrium position. The rotor
passes this position and deviates in the other direction to a stop. The spring makes
it again return to the equilibrium position, etc. Thus, the torsion oscillator performs
torsional vibrations from left to right relative to point 0.
An external torque T may be applied to the disk.
The physical parameters of the system characterizing the torsion oscillator: the
moment of inertia of the disk I, the spring stiffness k (torsion modulus), the damping
constant b (taking into account the viscous friction of the medium).
When the disk is rotated from the equilibrium position by an angle θ , a spiral
spring attached to it (the other end of which is fixed motionless) creates a returning
moment N proportional to the deflection angle:
127
Fig. 3.30 Torsion spring
oscillator
To describe real vibrational dynamical systems, some physical model is used,
which is called a linear or harmonic oscillator. This model introduces some basic
assumptions.
If the oscillator is once removed from the state of equilibrium, then a restoring
force will arise in such a system, which will tend to return the oscillator back to
the equilibrium position. The restoring force in magnitude is directly proportional to
the displacement and directed against the displacement. The physical quantities that
describe the oscillations of the oscillator change with time according to the harmonic
law of cosine or sine.
However, there are quite a lot of oscillatory systems to which the linear oscillator
model is applicable:
(a) spring pendulum—a load suspended on an elastic spring, which obeys Hooke’s
law at small displacements;
(b) the mathematical and physical pendulums that make small deviations from the
vertical in the gravitational field;
(c) an electric oscillatory circuit, consisting of a precharged capacitor, coil, and
resistor, which are connected in series in a circuit;
(d) torsion spring oscillator.
Let us consider it in more detail; see Fig. 3.30.
The oscillator consists of a disk (or rotor), which can rotate relative to a fixed axis
perpendicular to the plane in which the rotor is located. The rotor is engaged with a
weightless coil spring at one of its ends. The other end of the spring is rigidly fixed.
When the disk is rotated by a certain angle relative to point 0 (equilibrium position),
the spring, elastically deformed, twists, and the rotor stops in the extreme position.
Then the spring unwinds, returning the disk to the equilibrium position. The rotor
passes this position and deviates in the other direction to a stop. The spring makes
it again return to the equilibrium position, etc. Thus, the torsion oscillator performs
torsional vibrations from left to right relative to point 0.
An external torque T may be applied to the disk.
The physical parameters of the system characterizing the torsion oscillator: the
moment of inertia of the disk I, the spring stiffness k (torsion modulus), the damping
constant b (taking into account the viscous friction of the medium).
When the disk is rotated from the equilibrium position by an angle θ , a spiral
spring attached to it (the other end of which is fixed motionless) creates a returning
moment N proportional to the deflection angle: