Nā nīnau hoʻohālike resonance
ʻO ka resonance kahi hanana kino e kū mai ana i ka wā e koi ʻia ai kahi ʻōnaehana e haʻalulu ma kahi alapine kokoke a like paha me kona alapine kūlohelohe. Pono ka hoʻomaopopo hohonu ʻana i ka resonance e hoʻomaopopo piha ai pehea a me ke kumu o kēia hanana. I ke ola o kēlā me kēia lā, ʻike pinepine ʻia ka resonance ma nā ʻano like ʻole e like me ke mele, ka ʻenekinia, a me ka physics. E wehewehe kēia ʻatikala i ka resonance a hāʻawi i kekahi mau laʻana e kōkua iā mākou e hoʻomaopopo i ke kumumanaʻo.
He aha ka Resonance?
ʻO ke kani ʻana he hanana e kū mai ana i ka wā e haʻalulu ai kahi mea a ʻōnaehana paha me ka amplitude nui aʻe ma muli o ka loaʻa ʻana o nā haʻalulu mai kahi kumu ʻē aʻe i loaʻa ka alapine like a kokoke like paha me ke alapine maoli o ka mea. ʻO ke alapine kūlohelohe ke alapine e haʻalulu ai kahi ʻōnaehana i ka wā ʻaʻohe haunaele o waho.
Nā Laʻana o ke Resonance i ke Ola o kēlā me kēia lā
1. Ke kani ʻana o nā mea kani: Ke huki ʻia ke kaula kīkā, haʻalulu ia ma kahi alapine kūlohelohe kikoʻī, e hana ana i ke kani. Inā hoʻokokoke ʻia kahi ʻō hoʻonohonoho me ke alapine like, e hoʻomaka ka ʻō hoʻonohonoho e haʻalulu a hana i ke kani me ka ʻole o ka hoʻopā ʻia.
2. Ke kani ʻana o nā alahaka: I kekahi mau hihia, hiki i ke kani ʻana ke loaʻa nā hopena weliweli. ʻO kekahi laʻana, ʻo ia ka hiolo ʻana o ke alahaka ʻo Tacoma Narrows i ka makahiki 1940. Ua hoʻokumu nā makani i nā haʻalulu me ka alapine like me ke alapine maoli o ke alahaka, e hoʻoulu ai i ke alahaka e oscillate a hiki i ka hiolo ʻana.
3. Ke kani ʻana i loko o ke kīʻaha waina: ʻO ka ʻōwili ʻana i kahi manamana lima pulu a puni ka lihi o ke kīʻaha waina hiki ke hoʻoulu i ke aniani e haʻalulu i kona alapine kūlohelohe a hoʻopuka i ke kani. Inā kūlike ke kani hopena me ke alapine kūlohelohe o ke aniani, e piʻi aʻe ka amplitude o ka haʻalulu.
Nā nīnau hoʻohālike resonance
I kēia manawa ua maopopo iā kākou nā kumu o ke kani ʻana, e nānā kākou i kekahi mau pilikia hoʻohālike e hoʻomaʻamaʻa i ke kumumanaʻo.
Nīnau 1: Resonance i loko o kahi ʻōnaehana Spring-Mass
Ua kau ʻia kahi kaumaha o 2 kg mai ka hopena o kahi pūnāwai me kahi kūpaʻa pūnāwai o \(k = 50 \, \text{N/m}\). E helu i ke alapine kūlohelohe o kēia ʻōnaehana.
Hoʻonā:
Hiki ke helu ʻia ke alapine kūlohelohe o kahi ʻōnaehana puna-nui me ka hoʻohana ʻana i kēia ʻano hana:
\[ f_0 = \frac{1}{2\pi} \sqrt{\frac{k}{m}} \]
Ma hea:
– ʻO \( f_0 \) ke alapine kūlohelohe.
– ʻO \( k \) ke kūpaʻa puna.
– ʻO \( m \) ke kaumaha.
Ma ke komo ʻana i nā waiwai i ʻike ʻia:
\[ f_0 = \frac{1}{2\pi} \sqrt{\frac{50}{2}} \]
\[ f_0 = \frac{1}{2\pi} \sqrt{25} \]
\[ f_0 = \frac{1}{2\pi} \times 5 \]
\[ f_0 \approx \frac{5}{6.28} \approx 0.795 \, \text{Hz} \]
Nīnau 2: Resonance i ka Uila
Ma kahi kaapuni RLC me ke kū'ē \( R = 5 \, \Omega \), inductance \( L = 2 \, \text{H}\), a me ka capacitance \( C = 50 \, \text{µF}\), e helu i ke alapine resonant o ka ʻōnaehana.
Hoʻonā:
Hāʻawi ʻia ke alapine resonant i loko o kahi kaapuni RLC e:
\[ f_0 = \frac{1}{2\pi} \sqrt{\frac{1}{LC}} \]
Ma ke komo ʻana i nā waiwai i ʻike ʻia:
\[ f_0 = \frac{1}{2\pi} \sqrt{\frac{1}{2 \times 50 \times 10^{-6}}} \]
\[ f_0 = \frac{1}{2\pi} \sqrt{\frac{1}{0.0001}} \]
\[ f_0 = \frac{1}{2\pi} \times 100 \]
\[ f_0 \approx \frac{100}{6.28} \approx 15.92 \, \text{Hz} \]
Nīnau 3: Resonance i nā Mea Kani
He 0,5 mika ka lōʻihi o ke kaula a he 0,01 kg ke kaumaha. ʻO ke kaomi ma ke kaula he 100 N. E helu i ke alapine kūlohelohe o ke kaula ma ke ʻano kumu (n=1).
Hoʻonā:
Hāʻawi ʻia ke alapine kūlohelohe (kumu) o kahi kaula e ke ʻano:
\[ f_0 = \frac{1}{2L} \times \sqrt{\frac{T}{\mu}} \]
Ma hea:
– ʻO \( L \) ka lōʻihi o ke kaula.
– ʻO \( T \) ke anakahi uila.
– ʻO \( \mu \) ka nuipaʻa no kēlā me kēia anakahi lōʻihi (nuipaʻa/ (lōʻihi kaula)).
ʻO ka mea mua, e helu i ka nuipa no ka lōʻihi o ke anakahi:
\[ \mu = \frac{0.01}{0.5} = 0.02 \, \text{kg/m} \]
A laila, e hoʻokomo i nā waiwai i loko o ke ʻano alapine (frequency):
\[ f_0 = \frac{1}{2 \times 0.5} \times \sqrt{\frac{100}{0.02}} \]
\[ f_0 = 1 \times \sqrt{5000} \]
\[ f_0 = \sqrt{5000} \]
\[ f_0 = 70.71 \, \kikokikona{Hz} \]
Ka hopena
He mea koʻikoʻi ka hoʻomaopopo ʻana i ka resonance i nā ʻano aʻo like ʻole, e like me ke kino, ke mele, a me ka ʻenekinia. Ma ka hoʻomaopopo ʻana i ke kumumanaʻo kumu o ka resonance, hiki iā mākou ke hoʻohana iā ia no nā kumu maikaʻi, e like me ka hoʻomaikaʻi ʻana i ke ʻano kani o nā mea kani a i ʻole ka pale ʻana i ka pōʻino, e like me ka mea i hana ʻia i nā alahaka e ka resonance luku.
I ka hoʻoponopono ʻana i nā pilikia resonance, he mea nui e ʻike i nā palena āpau e pili ana i ka ʻōnaehana e kālailai ʻia nei. Ma ka hoʻomaopopo ʻana i nā alapine kūlohelohe a pehea e hana ai ka resonance, hiki iā mākou ke hana i nā wānana pololei, no nā kumu hana a me ka noiʻi ʻepekema. ʻAʻole wale ka resonance he manaʻo kumumanaʻo akā he hanana maoli e hoʻopilikia i nā ʻano he nui o ko mākou ola o kēlā me kēia lā.
