Forced Oscillations+ Resonance II final Part II Unit 01-Oscillation II Bihar Patna II 2025 скачать в хорошем качестве

Forced Oscillations+ Resonance II final Part II Unit 01-Oscillation II Bihar Patna II 2025

⏱️ TIMESTAMPS: 00:07 - Introduction to Forced Oscillations 00:50 - Factors Affecting the Amplitude of Forced Oscillation 01:48 - Formulas and Their Components 10:07 - Amplitude at Low Driving Frequency 13:58 - Amplitude at High Driving Frequency 16:42 - Definition of Resonance 26:36 - Resonant Frequency in the Presence of Damping 35:50 - The Resonant Curve with Zero Damping 37:37 - The Resonant Curve with Increasing Damping 38:26 - What is a Resonant Curve? A: Forced oscillation occurs when an external periodic force drives a system to oscillate at the frequency of the driving force, rather than its natural frequency. Unlike free oscillations (which decay due to damping), forced oscillations can persist indefinitely as long as the external force is applied. Q2: What is the difference between free oscillation and forced oscillation? Q3: What is resonance? How does it relate to forced oscillations? A: Resonance is a special case of forced oscillation where the driving frequency (ω ) matches the natural frequency (ω 0 ) of the system. At resonance, the system absorbs maximum energy from the driving force, resulting in the maximum amplitude of oscillation. Q4: Why does amplitude become maximum at resonance? A: At resonance, the phase difference between the driving force and the system’s displacement becomes zero. This means the force is always applied in the direction of motion — adding energy constructively with every cycle. Think of pushing a swing: if you push just as it reaches the highest point and moves back toward you, each push adds energy efficiently → big swings! In contrast: If you push too early or too late → some pushes oppose motion → less energy transfer. At resonance → perfect timing → maximum energy transfer → maximum amplitude. Q5: What is the role of damping in forced oscillations and resonance? A: Damping reduces the amplitude of oscillations over time. In forced oscillations: Low damping: Sharp, high peak in amplitude at resonance → system is “tuned” tightly. High damping: Broader, flatter resonance peak → less sensitive to frequency match → safer but less efficient. 📌 Practical implication: Bridges and buildings are designed with high damping to avoid catastrophic resonance (e.g., Tacoma Narrows Bridge collapse, 1940). Radio tuners use low damping to selectively pick up one frequency among many. Q6: What is a resonance curve (amplitude vs. frequency graph)? A ​ — radio receivers tune to stations via resonance Acoustic Sound waves resonating in a flute or organ pipe Optical Electrons in atoms absorbing photons at resonant frequencies → lasers Quantum Nuclear magnetic resonance (NMR), MRI scans Structural Skyscraper swaying during earthquake at matching frequency Q8: What are real-world applications and dangers of resonance? ✅ Applications: Radios & TVs: Tuning circuits resonate with specific broadcast frequencies. MRI Machines: Use nuclear magnetic resonance to image body tissues. Microwave Ovens: Resonate water molecules at 2.45 GHz to heat food. Musical Instruments: Body of guitar/violin resonates to amplify sound. Seismic Isolators: Designed to avoid resonance in earthquakes. ❌ Dangers: Tacoma Narrows Bridge (1940): Wind-induced vortices matched bridge’s natural frequency → catastrophic collapse. Engine Vibrations: If engine RPM matches chassis resonance → parts loosen or fail. Glass Shattering: Opera singer hits exact resonant frequency of wine glass → intense vibration → fracture. Q9: How do engineers prevent destructive resonance? A: Engineers use several strategies: Add damping (e.g., shock absorbers, rubber mounts) Change natural frequency (modify mass/stiffness) Use isolation pads to decouple vibrating components Avoid operating at critical frequencies (e.g., turbines run above/below resonance zone) Active control systems (sensors + actuators counteract vibrations in real-time)