Vibrations One Shot: Damping & Forced Vibration | Theory of Machines GATE | S K Mondal Sir

Mechanical Vibrations one-shot revision for GATE Mechanical Engineering (ME), ESE and PSUs by S K Mondal Sir (Ex-IES), part of Theory of Machines (TOM). Natural frequency by the static deflection method and the energy method, systems with pulleys, rods and rolling cylinders, damped free vibration (damping ratio, critical damping, damped natural frequency), torsional spring and damper systems, forced vibration, magnification factor, transmissibility and logarithmic decrement, all through GATE-type questions. Useful for: GATE ME & XE, ESE, ISRO, BARC, PSUs, SSC JE and RRB JE. ⏱️ Chapters 0:00 Revise India: Vibrations One Shot 1:34 Spring-Mass System & Static Deflection 3:09 When the Static Deflection Method Works 7:09 ωn = √(g/δ) 10:21 Advantage of the Static Deflection Method 12:46 Q: Natural Frequency of a Vibrating System 16:48 Q: Block, Pulley & Spring by the Energy Method 18:25 Kinetic Energy of the Pulley 21:36 Solid Disc: I = mr²/2 23:13 Converting Everything to θ 24:48 Differentiating the Energy Equation 28:42 Answer 30:16 Q: Rod with Masses Rotating About a Pivot 35:52 Parallel Axis Theorem 45:04 Energy Is Conserved: d/dt = 0 49:05 Q: Rolling Cylinder with Springs 52:12 I About the Instantaneous Centre 55:26 Natural Frequency Answer 58:05 Q: Massless Rod with Spring & Rope over a Pulley 1:00:31 CG Fixed: Only Rotation 1:02:58 CG Moves: Translation + Rotation 1:13:30 Answer & Finding the Calculation Error 1:17:18 Adding ml² About the Rotation Point 1:20:26 "Don't Touch" Questions in GATE 1:22:01 Damped Free Vibration 1:25:11 Overdamped, Critically Damped & Underdamped 1:27:29 Damping Ratio ζ = c/cc 1:28:22 Critical Damping Coefficient 1:29:11 Critically Damped: Fastest Return 1:31:31 Q: Largest Damping for Oscillatory Motion 1:34:42 Standard Form of the Equation 1:35:31 Q: Damping Coefficient of a System 1:41:01 Q: Damped Natural Frequency 1:42:44 ωd = ωn√(1 − ζ²) 1:43:32 Hz vs rad/s 1:45:09 Q: Static Deflection Method 1:50:34 Q: Rod with Two Springs & a Damper 1:52:10 D'Alembert's Principle 1:55:20 Damper Force Depends on Velocity 1:58:29 I About the Hinge 2:01:46 Critical Damping Condition 2:05:53 Answer 2:10:33 Break (Skip to 3:15:08) 3:15:08 Welcome Back 3:19:28 Q: Torsional Spring & Damper (Common Data) 3:20:16 Torsional Spring: Torque & Angle 3:24:58 Clockwise Moments Are Negative 3:26:28 Damper Moment About the Hinge 3:35:19 Comparing with the Standard Equation 3:37:37 Damping Coefficient Answer 3:39:55 Forced Vibration 3:43:04 Equation of Forced Vibration 3:43:55 Transient Then Steady State 3:45:32 Complementary Function + Particular Integral 3:48:39 Steady-State Amplitude 3:51:02 Magnification Factor 3:53:28 Transmissibility 3:55:13 What You Can Study with Mondal Sir 4:00:36 Logarithmic Decrement 4:01:24 Transmissibility Greater Than 1 4:03:46 Subscription Plans 4:06:13 Revisiting a Question: I About a Point 4:10:56 Three Methods, One Answer 4:13:13 Instantaneous Centre Method 4:14:49 Closing 📚 More Vibrations & Most Expected Questions: Vibrations Most Expected Questions:    • Vibrations Most Expected Questions | GATE ...   Fluid Mechanics Most Expected Questions Part 1:    • Fluid Mechanics Most Expected Questions Pa...   SOM One Shot: Most Important Topics:    • Strength of Materials One Shot: Mohr Circl...   📚 Theory of Machines & Vibrations Playlist:    • Theory of Machines & Vibrations for GATE &...   🎯 GATE 2027 subscription: https://unacademy.com/goal/Gate/QGFRK... Referral code: KHUSHRAHO 🏆 GATE Iconic Pro – Mondal Sir's Super 30 Batch: https://forms.gle/Y1JpUecSK2ZqitNEA 📢 Telegram: https://t.me/skmondalmaa #Vibrations #TheoryOfMachines #MechanicalEngineering