Mendefinisikan Gerak Harmonik Sederhana (GHS)
| English | Bahasa Indonesia |
|---|---|
| simple harmonic motion/ˈsɪmpl hɑːˈmɒnɪk ˈməʊʃn/ | gerak harmonik sederhana |
Pull a swing back and it always returns
- Pull a child's swing to one side and let go — it rushes back, overshoots, and swings the other way.
- The farther you pull it, the harder it is tugged back toward the middle.
- Any motion with this "always pulled back, in proportion" rule is simple harmonic motion 简谐运动 (SHM).
- It is the physics of springs, pendulums, guitar strings and atoms in a solid.
The defining rule
- SHM happens when the restoring force is proportional to the displacement from equilibrium, and points back toward it.
- In symbols: $F = -kx$ — the minus sign means "back toward the middle".
- Push it further out (bigger $x$) and the pull-back force grows in step.
- This single condition produces the smooth back-and-forth of every oscillator.
Gaya pemulih bertambah seiring perpindahan
Tarik pegas dan lihat gaya pemulih bertambah sebanding — inti dari GHS.
Pegas memiliki $k = 50\ \tfrac{\text{N}}{\text{m}}$. Berapa besar gaya pemulih pada perpindahan $0.2\ \text{m}$, dalam $\text{N}$?
$|F| = kx = 50 \times 0.2 = 10\ \text{N}$, mengarah kembali ke kesetimbangan.
Apa yang mendefinisikan gerak harmonik sederhana?
GHS memerlukan $F = -kx$: gaya pemulih sebanding dengan perpindahan, mengarah kembali ke kesetimbangan.
Dalam $F = -kx$, tanda minus berarti gaya mengarah ____ menuju kesetimbangan.
Gaya selalu berlawanan dengan perpindahan — ia mengarah kembali ke tengah.
Equilibrium and overshoot
- The oscillator has an equilibrium point where the net force is zero.
- Displaced, it is pulled back — but it arrives at equilibrium moving, so it overshoots.
- Then the restoring force slows it, stops it, and pulls it back again.
- The result is an endless, smooth oscillation about the middle.
Mengapa osilator GHS tidak berhenti begitu saja di titik kesetimbangan?
Di kesetimbangan gayanya nol tetapi kecepatannya maksimum, sehingga osilator melewatinya dan terus berayun.
Where SHM shows up
- A mass on a spring is the textbook example: $F = -kx$ exactly.
- A pendulum swings with SHM too, as long as the angle stays small.
- Atoms vibrating in a crystal, and a plucked string, are SHM as well.
- Whenever a system is nudged from a stable balance, SHM tends to appear.
Ayunan adalah gerak harmonik sederhana hanya untuk sudut ayunan kecil.
Gaya pemulih sebanding dengan perpindahan hanya pada sudut kecil; ayunan besar bukan GHS.
Pilih semua sistem yang mengalami gerak harmonik sederhana (setidaknya secara perkiraan).
Pegas, bandul sudut kecil dan tali semuanya memiliki gaya pemulih $\propto$ simpangan. Penggerak kecepatan konstan tidak.
A pendulum is only approximately SHM — the restoring force is proportional to displacement only for small angles. Swing it too far and the motion is no longer simple harmonic. The mass-on-a-spring is the cleaner ideal.
A spring pulls back with $F = -kx$, where $k = 50\ \tfrac{\text{N}}{\text{m}}$. Find the restoring force at a displacement of $0.2\ \text{m}$.
- $F = -kx = -50 \times 0.2 = -10\ \text{N}$.
The $10\ \text{N}$ force points back toward equilibrium, opposite the displacement.
Simple harmonic motion is oscillation where the restoring force is proportional to displacement and points back to equilibrium: $F = -kx$. The object overshoots equilibrium and swings endlessly. Springs are exact SHM; pendulums are SHM only for small angles.