Ngā Tauira Pātai Whakaohooho
Ko te haruru he āhuatanga ā-tinana e puta ana ina akiakihia tētahi pūnaha kia wiri i te auau e tata ana, e ōrite ana rānei ki tōna auau tūturu. Me mārama ake ki te haruru kia tino mārama ai ki te āhua me te take o tēnei āhuatanga. I roto i te oranga o ia rā, he maha ngā wā ka kitea te haruru i roto i ngā momo mara pērā i te puoro, te hangarau, me te ahupūngao. Ka whakamāramahia e tēnei tuhinga te haruru, ā, ka whakaratohia he tauira hei āwhina i a tātou ki te mārama ki te ariā.
He aha te Āhuatanga?
Ko te haruru he āhuatanga e puta ana ina wiri te mea, te pūnaha rānei me te kaha nui ake nā te whiwhinga wiri mai i tētahi atu pūtake he rite te auau, he tata rite rānei ki te auau tūturu o te mea. Ko te auau tūturu ko te auau e wiri ai te pūnaha i te wā kāore he raruraru o waho.
Ngā Tauira o te Āhuatanga i roto i te Oranga o Ia Rā
1. Te Āhuatanga o ngā Taonga Puoro: Ina tangohia te aho kitā, ka wiri i tētahi auau tūturu, ka puta he oro. Ki te whakatatahia mai tētahi marau whakaōrite o taua auau, ka tīmata te wiri o te marau whakaōrite, ka puta he oro, me te kore e pāngia.
2. Te Whakaohooho i roto i ngā Piriti: I ētahi wā, ka pā kino te whakaohooho. Ko tētahi tauira ko te hinganga kino o te Piriti o Tacoma Narrows i te tau 1940. Nā ngā hau pupuhi i hanga he wiri me te auau rite ki te auau tūturu o te piriti, ka meinga te piriti kia wiriwiri tae noa ki te hinganga.
3. Te Hāora i roto i te Karāhe Waina: Mā te huri i te matihao mākū ki te taha o te karāhe waina ka wiri te karāhe i tōna auau tūturu, ā, ka puta he oro. Mēnā ka ōrite te oro e puta mai ana ki te auau tūturu o te karāhe, ka piki ake te kaha o te wiri.
Ngā Tauira Pātai Whakaohooho
Nā te mea kua mārama tātou ki ngā kaupapa matua o te orooro, me titiro tātou ki ētahi tauira rapanga hei whakaharatau i te ariā.
Pātai 1: Te Āhuatanga i roto i te Pūnaha Puna-Mass
E iri ana tētahi papatipu 2 kg i te pito o tētahi puna me te pūmau puna o \(k = 50 \, \text{N/m}\). Tātaihia te auautanga maori o tēnei pūnaha.
Otinga:
Ka taea te tatau i te auau ā-tūroa o tētahi pūnaha puna-papatipu mā te whakamahi i te tātai e whai ake nei:
\[ f_0 = \frac{1}{2\pi} \sqrt{\frac{k}{m}} \]
Dimana:
– Ko te auautanga maori te \( f_0 \).
– Ko te pūmau puna ko \( k \).
– Ko te papatipu ko te \( m \).
Mā te whakauru i ngā uara e mōhiotia ana:
\[ f_0 = \frac{1}{2\pi} \sqrt{\frac{50}{2}} \]
\[ f_0 = \frac{1}{2\pi} \sqrt{25} \]
\[ f_0 = \frac{1}{2\pi} \whakareatia ki te 5 \]
\[ f_0 \approx \frac{5}{6.28} \approx 0.795 \, \text{Hz} \]
Pātai 2: Te Āhuatanga o te Hiko
I roto i tētahi ara iahiko RLC he ātete \( R = 5 \, \Omega \), he inductance \( L = 2 \, \text{H}\), me he capacitance \( C = 50 \, \text{µF}\), tatauhia te auau orooro o te pūnaha.
Otinga:
Ko te auau āwhati i roto i te ara iahiko RLC ka hoatuhia e:
\[ f_0 = \frac{1}{2\pi} \sqrt{\frac{1}{LC}} \]
Mā te whakauru i ngā uara e mōhiotia ana:
\[ f_0 = \frac{1}{2\pi} \sqrt{\frac{1}{2 \times 50 \times 10^{-6}}} \]
\[ f_0 = \frac{1}{2\pi} \sqrt{\frac{1}{0.0001}} \]
\[ f_0 = \frac{1}{2\pi} \whakareatia ki te 100 \]
\[ f_0 \approx \frac{100}{6.28} \approx 15.92 \, \text{Hz} \]
Pātai 3: Te Whakaoho i roto i ngā Taonga Puoro
He 0,5 mita te roa o tētahi aho, ā, he 0,01 kg te taumaha. Ko te kukū o te aho he 100 N. Tātaihia te auautanga maori o te aho i te aratau taketake (n=1).
Otinga:
Ko te auau tūturu (taketake) o te aho ka hoatuhia e te tātai:
\[ f_0 = \frac{1}{2L} \times \sqrt{\frac{T}{\mu}} \]
Dimana:
– Ko te \( L \) te roa o te aho.
– Ko te ngaohiko te \( T \).
– Ko te papatipu mō ia waeine roa (papatipu/ (roa aho)) te \( \mu \).
Tuatahi, tatauhia te papatipu mō ia waeine roa:
\[ \mu = \frac{0.01}{0.5} = 0.02 \, \text{kg/m} \]
Kātahi ka monohia ngā uara ki te tātai auau:
\[ f_0 = \frac{1}{2 \times 0.5} \times \sqrt{\frac{100}{0.02}} \]
\[ f_0 = 1 \times \sqrt{5000} \]
\[ f_0 = \sqrt{5000} \]
\[ f_0 = 70.71 \, \kuputuhi{Hz} \]
Whakamutunga
He mea nui te mārama ki te haruru i roto i ngā momo marautanga, pērā i te ahupūngao, te puoro, me te hangarau. Mā te mārama ki te ariā taketake o te haruru, ka taea e tātou te whakamahi mō ngā kaupapa pai, pērā i te whakapai ake i te kounga oro o ngā taonga puoro, te ārai rānei i ngā kino, pērā i ngā mea i pā ki ngā piriti e te haruru whakangaro.
I te whakaoti rapanga orooro, he mea nui kia tautuhia ngā tawhā katoa e pā ana ki te pūnaha e tātarihia ana. Mā te mārama ki ngā auau taiao me te mahi a te orooro, ka taea e tātou te matapae tika, mō ngā kaupapa mahi me ngā rangahau pūtaiao. Ehara te orooro i te ariā noa iho engari he āhuatanga tūturu e pā ana ki ngā āhuatanga maha o tō tātou oranga o ia rā.
