11TH GRADE · OSCILLATIONS AND WAVES
Mechanical vibrations
Period, frequency, phase, speed, acceleration and energy.
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Basic Concepts
Hesitation
A time-repeated change in the state of a system near its equilibrium position.
The system goes through the same states repeatedly, and energy usually passes between two forms.
Harmonic oscillation
An oscillation in which a quantity changes according to the law of sine or cosine.
The restoring acceleration is directed against the displacement and is proportional to it; therefore the graph has a sinusoidal shape.
Physical quantities
Oscillation period
Time of one complete oscillation.
Unit: second ·
Oscillation frequency
The number of complete oscillations per unit of time.
Unit: hertz ·
Number of oscillations
The number of complete oscillations completed.
Unit: dimensionless quantity
Cyclic frequency
The speed of change in the phase of oscillation.
Unit: radians per second ·
Pendulum length
The distance from the suspension point to the center of mass of the load.
Unit: meter ·
Cargo weight
The mass of a body oscillating.
Unit: kilogram ·
Spring stiffness
Spring deformation resistance coefficient.
Unit: newton per meter ·
Offset
Deviation from the equilibrium position.
Unit: meter ·
Offset amplitude
Largest displacement modulus.
Unit: meter ·
Initial phase
Oscillation phase at the initial moment.
Unit: radian ·
Speed amplitude
The highest modulus of speed during oscillation.
Unit: meter per second ·
Acceleration amplitude
The largest acceleration module during oscillation.
Unit: meters per second squared ·
Energy of vibrations
Total mechanical energy of an ideal oscillator.
Unit: joule ·
Lesson formulas
Period through observation time
The period is equal to the time divided by the number of oscillations and is the inverse of the frequency.
Oscillation frequency
Frequency is equal to the number of oscillations per time and the inverse of the period.
Hertz definition
One hertz corresponds to one vibration per second.
Cyclic frequency
The cyclic frequency is equal to the change in phase per unit time.
Period of a mathematical pendulum
The period of small oscillations depends on the length of the pendulum and the acceleration of gravity.
Condition: The oscillations are small, air resistance and the mass of the thread are neglected.
Period of a spring pendulum
The period depends on the mass of the load and the stiffness of the spring.
Equation of harmonic vibration
The displacement varies harmonically with phase.
Speed amplitude
The maximum speed is equal to the product of the displacement amplitude and the cyclic frequency.
Acceleration amplitude
The maximum acceleration is equal to the displacement amplitude times the square of the cyclic frequency.
Energy of a mechanical oscillator
The total energy is expressed in terms of the maximum velocity or displacement amplitude.
Related formulas
The same formulas in the reference, with symbols and units.
Tasks on the topic
Statements, answer options and the walkthrough.