Forced Vibrations

• Occur when an oscillating system is driven by another oscillator.
• Example: A mass-spring oscillator being driven by an electric motor.
• The driving frequency doesn't have to match the system's natural frequency.

Resonance

• Happens when the driving frequency matches the natural frequency of the system.
• Leads to very large amplitudes, sometimes even breaking the system.
• Can be explained through conservation of energy.

Damping

• Affects the amplitude and phase of vibrations.
• Submerging the mass in water, oil, or other viscous liquids can provide damping.
• Influences the sharpness of the transition from in-phase to out-of-phase vibrations.

Pushing a Child on a Swing

• Imagine you're pushing a child on a swing. For maximum efficiency, you need to push at the right moment in the cycle (at the child's fastest point) and at the correct rate. This is like the driver (you) being 90° ahead of the driven system (swing) itself.

Barton's Pendulum

• A heavy pendulum (driver) drives lighter pendulums (driven) of varying lengths.
• The pendulum with the same length as the driver oscillates with the greatest amplitude and is 90° behind the driver.
• Pendulums with different lengths have smaller amplitudes and different phase relationships with the driver.

Blade and Electromagnet

• A blade clamped at one end lies close to an electromagnet powered by a variable-frequency signal generator.
• Resonance effects can be observed by varying the signal generator frequency and blade length.
• Damping effects can be studied by adding strips of card to the blade to increase air resistance.

• Resonance of gas molecules can be used to model the greenhouse effect.
• Certain frequencies of light resonate with certain gas molecules, leading to energy absorption and heat retention in the atmosphere.