Slide 1
Driving near a natural frequency can build resonance
A system that oscillates has characteristic natural frequencies. Driving near one of them can produce a large response called resonance.
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A swing illustrates the timing: modest pushes delivered at the right part of each cycle add energy repeatedly. Poorly timed pushes can remove energy or fail to build a large motion.
Slide 2
Stiffness and mass set a spring’s natural frequency
For a simple mass and spring, greater stiffness raises the natural frequency. Greater mass lowers it under otherwise equal conditions.
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The motion exchanges elastic potential energy with kinetic energy. The cycle time depends on how strongly displacement produces a restoring force and how much inertia resists the resulting acceleration.
Slide 3
Damping removes energy and limits the peak
Friction and other losses remove energy from oscillation. Greater damping usually lowers and broadens the resonance peak.
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Without sustained driving, a damped oscillator gradually settles. Under steady driving, its eventual amplitude reflects a balance between energy supplied each cycle and energy dissipated into other forms.
Slide 4
One object can resonate in several modes
Strings, air columns and structures can resonate in several patterns. Each mode has its own arrangement of motion and frequency.
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A standing wave contains nodes with little motion and regions of greater motion. Boundary conditions, such as fixed string ends or open pipe ends, select which patterns are possible.
Slide 5
Resonance can strengthen music or damage machinery
Musical instruments use resonance to strengthen selected vibrations. Machines may need damping or changed stiffness to avoid excessive motion.
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Changing a system’s mass or stiffness can move a natural frequency away from a repeated driving force. Reducing the forcing itself is another option; adding material without analysing the mode is not a universal solution.
Sources
- Sound Waves and the Physics of Music
The Physics Classroom
- Anatomy of an Electromagnetic Wave
NASA