6. Resonance Flashcards
(44 cards)
What is elasticity?
a solid body is called elastic, if upon deformation by external forces such forces emerge in the body that tend to restore its original shape.
what is elastic deformation?
The spring constant can be calculated from t the change of the external force acting on the body and the deformation
- ∆Fext is the the change of the external force
- ∆x is the deformation
- k is the spring constant.
What is Hook’s law formula?
F = -k x
F is the (pulling, pressing, bending etc.) restoring force emerging in the body
x is the deformation,
k is the spring constant
What do vibration, swinging, or oscillation refer to?
a repeating motion, variation, displacement around the equilibrium value of a physical, chemical, or biochemical variable.
-> a phenomenon where a quantity varies in time about an equilibrium value.
What is SIMPLE HARMONIC OSCILLATION?
An oscillation is harmonic, if the temporal change of the variable is sinusoidal.
→ Such oscillation forms if the restoring force bringing the system back to equilibrium is proportional to the displacement and directed towards the equilibrium position.
Simple harmonic oscillation can be related to uniform ___ motion
circular
The motion of a point-like object is called simple harmonic oscillation, if the restoring force, which drives the motion back towards the equilibrium position, is directly proportional to the displacement → The time dependence of the displacement is_____
Sinusoidal
Simple harmonic oscillation can be related to uniform circular motion.
→ Consider a point rotating along a circle of radius R with constant angular velocity (Fig. 2).
→ The vertical projection of the rotating point on a straight line is a simple harmonic motion ___, such as the motion of mass m on a spring displaced from its equilibrium position
up and down
What is AMPLITUDE?
the maximum displacement of an oscillation from the equilibrium position (within a period).
Simple harmonic oscillation can be related to uniform circular motion.
→ Consider a point rotating along a circle of radius R with constant angular velocity (Fig. 2). The vertical projection of the rotating point on a straight line is a simple harmonic motion up and down, such as the motion of mass m on a spring displaced from its equilibrium position (Fig. 2, states a - f ).
→ In this case the maximum displacement, i.e., the amplitude of the oscillation is: ___
A = R.
Simple harmonic oscillation is characterized by __ (2 things)
- the eigenfrequency f0 (also called natural frequency)
- the time period T = 1/f0.
What is EIGENFREQUENCY, NATURAL FREQUENCY?
- the frequency at which a free oscillatory system oscillates.
- Eigenfrequency is independent of the displacement; its value is defined only by the characteristics of the system.
SIMPLE HARMONIC OSCILLATION
The periodic displacements during the oscillation are accompanied by the ___
Interconversion of different forms of energy characteristic for the oscillatory system
SIMPLE HARMONIC OSCILLATION
. In an ideal oscillatory system (i.e., those working without loss of energy), the sum of these energies is __
Sinusoidal
In case of a resonance circuit
Describe the sum of energies occurring
In case of a resonance circuit the sum of the magnetic energy of the inductor coil and the electric energy of the capacitor is constant
Meaning of this equation
If displacement x and time t are measured from the state of equillibrium (a), then the displacement of the oscillating mass at phase angle = t can be described by the following equatio
What is UNDAMPED FREE OSCILLATION?
oscillation without energy loss (e.g., without friction). → As a result, the amplitude of the oscillation is constant.
If the spring–mass oscillatory system mentioned in the previous example is free of friction, then the mass displaced from its resting state to x = A will go through an (1)___ (Fig. 3) with (2)___ amplitude for an (3)___ time.
- undamped free oscillation
- constant
- infinite
If the spring–mass oscillatory system mentioned in the previous example is free of friction, then the mass displaced from its resting state to x = A will go through an undamped free oscillation (Fig. 3) with constant amplitude for an infinite time.
→ In this ideal case, the oscillation is characterized by ____
a single line of amplitude A at the given eigenfrequency f0 in the frequency–amplitude plot (spectrum)
UNDAMPED FREE OSCILLATION
In this ideal case, the oscillation is characterized by a ___ line of amplitude A at the given eigenfrequency f0 in the frequency–amplitude plot (spectrum) shown on the right side of the Fig. 3.
single
UNDAMPED FREE OSCILLATION
In this ideal case, the oscillation is characterized by a single line of amplitude A at the given ___ in the frequency–amplitude plot (spectrum) shown on the right side of the Fig. 3.
eigenfrequency
UNDAMPED FREE OSCILLATION
In this ideal case, the oscillation is characterized by a single line of amplitude A at the given eigenfrequency f0 in the___ shown on the right side of the Fig. 3.
frequency–amplitude plot (spectrum)
What is DAMPED FREE OSCILLATION?
scillation with energy loss (e.g., friction).
→ As a result, the amplitude of the oscillation decays with time.
DAMPED FREE OSCILLATION
In real life, (1)___ is always present, thus the energy of the oscillatory system is gradually (2)___, and the amplitude of the oscillation (3)___.
- friction
- dissipated (i.e., it turns into heat)
- decreases
