University Differential Equations Mechanical Vibrations and Electric Circuits — Unit Notes
Every definition and theorem this unit expects you to know, stated once each and written to be revised from: 4 definitions and 6 theorems, 5 worked examples, 3 diagrams, in 13 printable pages. This page lists what the notes cover. The notes themselves come with the University Differential Equations bundle.
Unit notes — in the bundle
Not sold separately. The practice worksheet for this unit is free, with no email and no account.
Mechanical Vibrations and Electric Circuits — what the notes cover
6 sections, in the order the unit is taught. Each entry below is the title of a definition or a theorem the notes state in full.
What you need
Also in this section: 1 note on method and common errors.
Free undamped motion in amplitude and phase form
- Definition — Free undamped motion
- Theorem — Amplitude and phase form
Also in this section: 1 worked example, 1 note on method and common errors, 1 diagram.
Free damped motion and the three damping cases
- Definition — Free damped motion and the three cases
- Theorem — The underdamped solution and its envelope
Also in this section: 1 worked example, 1 note on method and common errors, 1 diagram.
Driven motion with transient and steady-state terms
- Definition — Driven motion: transient and steady state
- Theorem — The steady-state response to a sinusoidal force
Also in this section: 1 worked example, 1 note on method and common errors.
Resonance
- Theorem — Pure resonance
- Theorem — The peak of the steady-state amplitude
Also in this section: 1 worked example, 1 note on method and common errors, 1 diagram.
Series circuits with resistance, inductance and capacitance
- Definition — The series circuit equation
- Theorem — The circuit and the spring are the same equation
Also in this section: 1 worked example, 1 note on method and common errors.
Where the notes are
The notes are one of the documents in the University Differential Equations Solutions Bundle, beside the unit test, the challenge problems and every worked answer key. The Mechanical Vibrations and Electric Circuits practice worksheet is free and stays free.
Every University Differential Equations topic — the complete Solutions Bundle
One download, one payment, the whole program. For all 9 University Differential Equations units: the worksheet, the reference notes, the challenge set, the unit test and every answer key — these notes included.
- Worked solutions, not answer lists — every step written out
- Covers the whole year's program at this level
- Less than the price of one hour of tutoring — for the entire year's solutions
Practise it, then test yourself
Notes on their own do not make anything stick. This unit has a free, printable practice worksheet, and an end-of-unit test that comes with the bundle.
Mechanical Vibrations and Electric Circuits practice worksheet About the Mechanical Vibrations and Electric Circuits unit test