Are these Mechanical Vibrations handwritten notes free?

Yes. Fill in the short form on this page and the PDF downloads right away. There is no charge.

Are these official university notes?

No. These are original Uncodemy revision notes for Mechanical Vibrations. They are not issued by AKTU or any other university and are not a copy of university material.

Which syllabus do the Mechanical Vibrations notes follow?

They follow the common topics of Indian B.Tech Mechanical syllabi for Mechanical Vibrations. Unit names and order differ by university, so check your own syllabus and skip or add topics as needed.

Do the notes cover two degree of freedom systems?

Yes, in short. Unit 8 covers two DOF systems and vibration measuring instruments. Check your syllabus for multi-DOF topics.

What is the most important formula in vibrations?

Natural frequency equals the square root of stiffness over mass. Most other results build on it, so learn it with its meaning.

Is critical speed of shafts included?

Yes. Unit 7 covers whirling of shafts, critical speed from static deflection and Dunkerley's method.

Mechanical Vibrations Handwritten Notes PDF

Key takeaways

Original Uncodemy revision notes in 8 units plus a practice question list.
Worked examples on natural frequency from static deflection, a damped spring-mass system and transmissibility.
Natural frequency, damping ratio and transmissibility questions appear in most papers.
Not official university notes. Check your own syllabus; vibrations is sometimes a unit of Dynamics of Machines.
Free download after a short form.

About these Mechanical Vibrations notes

These are original Uncodemy revision notes for Mechanical Vibrations, written by the Uncodemy trainer team in a clean handwritten style. They follow the topics found in the common Indian B.Tech Mechanical syllabus. They are not official university notes, not a textbook and not a copy of any university's material. Unit names, order and depth differ between universities (AKTU, state technical universities and autonomous colleges all use their own scheme), so check your own syllabus and tick the units you need before you start.

Vibrations is taught either as a separate subject or as part of Dynamics of Machines. The notes build each unit on the single degree of freedom spring-mass model, so the later units are easy to follow.

Each unit has short definitions, key formulas in highlighted boxes, comparison tables, "remember" points and worked examples with the steps shown. A list of commonly asked practice questions closes the notes. These are practice questions based on common syllabus topics, not verified past papers.

What's inside the Mechanical Vibrations notes

The PDF has 8 units plus a practice question list. Here is what each unit covers, so you can match it with your syllabus.

Unit 1: Basics

Terms: period, frequency, amplitude, degrees of freedom and resonance.
Types of vibration: free, forced, damped, undamped, linear and torsional.

Unit 2: Undamped Free Vibration

Methods to find natural frequency: equilibrium, energy and Rayleigh's methods.
Equivalent springs: springs in series and parallel.
Other single DOF systems: simple and compound pendulum and similar systems.

Unit 3: Damped Free Vibration

Viscous damping: under, critical and over damping and the damping ratio.
Logarithmic decrement: finding damping from successive amplitudes.
Coulomb damping: dry friction damping and how it differs from viscous damping.

Unit 4: Forced Vibration

Harmonic excitation: magnification factor and phase angle.
Rotating unbalance and base excitation: two common real cases of forced vibration.

Unit 5: Vibration Isolation and Transmissibility

Transmissibility: force and motion transmissibility and why the frequency ratio must exceed root 2 for isolation.

Unit 6: Torsional Vibration

Single and two-rotor systems: natural frequency and node position.

Unit 7: Whirling of Shafts

Critical speed: critical speed from static deflection and Dunkerley's method.

Unit 8: Two DOF Systems and Measurement

Two DOF systems: natural frequencies and mode shapes in short.
Vibration measuring instruments: vibrometer and accelerometer basics.

How to revise Mechanical Vibrations

Almost every vibrations problem reduces to finding stiffness, mass and damping. Practise that first.

Master equivalent stiffness: series and parallel springs and beams treated as springs.
Memorise the core formulas with meaning: natural frequency, damping ratio, damped frequency, log decrement, magnification factor and transmissibility.
Sketch the response curves: magnification factor and transmissibility curves versus frequency ratio.
Use the energy method: it is often the fastest way to find natural frequency of a new system.
Redo the worked numericals: they cover free, damped and forced cases.

Exam focus: high-weightage Mechanical Vibrations topics

These topics are common across syllabi:

Natural frequency by equilibrium, energy and Rayleigh's methods.
Damping ratio, logarithmic decrement and damped natural frequency.
Magnification factor and phase angle in forced vibration.
Transmissibility and vibration isolation.
Two-rotor torsional systems and critical speed of shafts.

Typical numericals worked in the notes

Machine with 2 mm static deflection on its springs: natural frequency works out to about 11.15 Hz.
Spring-mass-damper with m = 10 kg, k = 4000 N/m, c = 80 N s/m: natural frequency, damping ratio, damped frequency and amplitude ratio.
A 100 kg machine on springs running at 600 rpm: find transmissibility.

Use the scientific calculator for square roots and logarithms and the unit converter to switch between rpm, rad/s and Hz.

A 7-day revision plan for Mechanical Vibrations

Use this plan in the week before your exam, after you have studied the subject once in class. Spend about two to three hours a day.

Day 1: Unit 1 (Basics), Unit 2 (Undamped Free Vibration). Read, close the PDF, then write the key formulas and definitions from memory.
Day 2: Unit 3 (Damped Free Vibration), Unit 4 (Forced Vibration). Read, close the PDF, then write the key formulas and definitions from memory.
Day 3: Unit 5 (Vibration Isolation and Transmissibility), Unit 6 (Torsional Vibration). Read, close the PDF, then write the key formulas and definitions from memory.
Day 4: Unit 7 (Whirling of Shafts). Read, close the PDF, then write the key formulas and definitions from memory.
Day 5: Unit 8 (Two DOF Systems and Measurement). Read, close the PDF, then write the key formulas and definitions from memory.
Day 6: redo every worked example in the notes without looking at the solution, then check each step.
Day 7: attempt the practice question list at the end of the PDF in exam time, then go back to the units where you got stuck.

Who these notes are for

B.Tech semester exams: third- and final-year Mechanical students preparing for Mechanical Vibrations or Dynamics of Machines papers.
GATE ME basics: GATE ME regularly asks natural frequency, damping ratio, magnification factor and transmissibility questions. The notes cover basics and standard formulas; for GATE you still need a full question bank and previous papers from the official GATE site.
Interviews: design, testing and automotive NVH roles often ask about resonance, damping and vibration isolation.
Diploma and lateral-entry students: the plain language and worked steps make the units easy to follow, but check which topics are in your own scheme.

How to use these notes with your textbook

These notes are short on purpose. They are meant for revision, not for learning Mechanical Vibrations for the first time. Study each unit once from your class notes, a standard textbook or the matching NPTEL course, and then use the PDF to revise quickly. If a topic in your syllabus is missing from the notes, mark it in your syllabus copy and study it from your textbook. If your teacher uses a different method or notation, follow your teacher in the exam. You can also request notes for another subject through the Uncodemy handwritten notes request page.

Download Mechanical Vibrations Handwritten Notes PDF