9TH GRADE · MECHANICAL VIBRATIONS
Oscillation parameters and pendulums
Amplitude, period, frequency, phase, mathematical and spring pendulums.
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Basic Concepts
Oscillatory system
The system is capable of repeatedly moving around a stable equilibrium position due to the restoring effect and inertia.
The pendulum and the mass on the spring exchange kinetic and potential energy.
Amplitude, period and frequency
Amplitude specifies the maximum deviation, period specifies the cycle time, and frequency specifies the number of cycles per second.
Period and frequency are reciprocal; parameters are measured over several oscillations to reduce the relative error.
Mathematical and spring pendulums
A mathematical pendulum models a small body on a string, and a spring pendulum models a load connected to an elastic spring.
The period of the first depends on the length and g, and the second - on the mass of the load and the stiffness of the spring.
Physical quantities
Amplitude
Maximum absolute deviation from the equilibrium position.
Unit: meter ·
Period
Time of one complete oscillation.
Unit: second ·
Frequency
The number of complete oscillations per unit of time.
Unit: hertz ·
Pendulum length
The distance from the suspension point to the center of mass of the load.
Unit: meter ·
Lesson formulas
Period according to the number of oscillations
The period is equal to the entire observation time divided by the number of oscillations.
Frequency
Frequency is equal to the number of oscillations per time and the inverse of the period.
Period of a mathematical pendulum
For small oscillations, the period depends on the length of the pendulum and the acceleration of gravity.
Period of a spring pendulum
The period increases with the mass of the load and decreases with the stiffness of the spring.
Related formulas
The same formulas in the reference, with symbols and units.
Tasks on the topic
Statements, answer options and the walkthrough.