ME20 · Sem 5 · Dynamics of machinery

Forced vibration and resonance

Aim: Measure the amplitude of a spring–mass system near resonance.

🧪 Live simulation🧊 Real-time 3D bench⚠ Simulated values, not physical measurements

🔬 Virtual lab

Starting the lab…

📘 Theory

A spring–mass–damper excited at frequency f vibrates with amplitude (F0/k)/√((1 − r²)² + (2ζr)²), where r = f/fn. At resonance (r = 1) only damping limits the amplitude.

fn = √(k/m)/2π · X/(F0/k) = 1/√((1 − r²)² + (2ζr)²)

🧰 Apparatus (virtual)

Spring–mass rig
shaker
accelerometer

📝 Procedure

Sweep the forcing frequency towards fn
Read the amplitude at resonance
Compare with F0/(2ζk)
Raise the stiffness and see fn move

Observations and result (kept on this device)

🎤 Viva questions

Why did the Tacoma Narrows bridge fail

Aerodynamic flutter fed energy into a natural mode.

How do engineers avoid resonance

Keep running speeds away from natural frequencies and add damping.

🛡️ Safety

Virtual by default. Machine shops, CNC, presses and test rigs need instructor supervision, PPE and machine-specific safety training.