Maren pushes her little cousin on a playground swing. Small pushes, timed with the swing, and the ride climbs higher and higher.
Timing is the whole trick. The same pushes, badly timed, get almost nothing. This lesson names what the matched timing does.
A swing is an oscillator with a natural frequency: tapped once and left alone, it swings at that one rate.
Maren pushes in time with the swing, so her driving frequency matches the swing's natural frequency.
Each push lands just as the swing starts moving away from her, and each push transfers energy to the swing at just the right moment.
Push after push, the amplitude grows: the swing climbs higher each cycle.
Driven at any other frequency, the mistimed pushes slow the swing as often as they speed it, and the amplitude stays small.
When a system is driven at its natural frequency, its oscillation builds up to a large amplitude. This build-up is called resonance.
Any driven oscillation is a forced vibration; resonance is the special case where the driving frequency matches the natural frequency and the amplitude builds up large.
A diving board, pressed once and released, springs at 2 Hz. Noll bounces gently on its end exactly 2 times each second, and each bounce takes him higher. Name what is happening, and say why the amplitude grows.
The board's natural frequency is 2 Hz, and Noll drives it at 2 Hz: the frequencies match.
Energy transfers to an oscillator most efficiently when the driving frequency matches its natural frequency.
So each bounce adds to the board's motion, and the amplitude builds up.
The board is resonating: driven at its natural frequency, its amplitude grows large.
A diving board's natural frequency is 2 Hz. Pim pushes its end down 5 times each second. Describe the board's response.
The driving frequency, 5 Hz, does not match the board's natural frequency, 2 Hz.
Mistimed pushes slow the board as often as they speed it.
The board only trembles: a small forced vibration, with no build-up.
A footbridge sways gently on its own at 1 Hz. A crowd's steps land on it once each second, in time with the sway. What happens to the bridge's swaying?
Pim says: 'A swing pushed in time with its own swinging builds up a large amplitude, because the pushing frequency matches its natural frequency.' Is Pim correct?
A system driven at its natural frequency builds up a large amplitude. What is this build-up called?
A rope bridge sways higher and higher as hikers' steps land in time with its natural sway. Which option explains the build-up?
Maren pushes a porch swing at random moments, some early, some late. Which statement is correct?
Which situation is resonance?