1. E rua ngā pendulum māmā kei ngā wāhi rerekē e rua. Ko te roa o te pendulum tuarua he 0.4 ngā wā o te roa o te pendulum tuatahi, ā, ko te whakaterenga o te kaha ā-papatipu e pā ana ki te pendulum tuarua he 0.9 ngā wā o te whakaterenga o te kaha ā-papatipu e pā ana ki te pendulum tuatahi. Whakatauhia te whakataurite i te auau o te pendulum tuatahi ki te pendulum tuarua.
A. 2/3
B. 3/2
C. 4/9
D. 9/4
Mōhiotia:
Ko te roa o te taura o te pendulum tuatahi (l 1 ) = 1
Ko te roa o te taura o te pendulum tuarua (l 2 ) = 0.4 (l 1 ) = 0.4 (1) = 0.4
Te whakaterenga nā te kaha o te pendulum tuatahi (g 1 ) = 1
Te whakaterenga nā te kaha o te taumaha o te pendulum tuarua (g 2 ) = 0.9 (1) = 0.9
E hiahiatia ana: Te whakataurite i te auau o te pendulum tuatahi (f 1 ) ki te pendulum tuarua (f 2 )
Rongoā:
Te whakataurite i te auau o te pendulum tuatahi (f 1 ) ki te pendulum tuarua (f 2 ):
Ko te whakautu tika ko A.
2. Ka iri tētahi mea i tētahi pito o te taura , kātahi ka mahi i tētahi nekehanga harmony māmā me te auau o te 0.5 Hertz. Mēnā ka whakanuia te roa o te taura kia whā ngā wā i te roa tīmatanga, tātaihia te wā o te nekehanga harmony.
A. ¼ hēkona
B. ½ hēkona
C. 2 hēkona
D. 4 hēkona
Mōhiotia:
Auautanga o te pendulum (f) = 0.5 Hz
E hiahiatia ana: Tāutuhia te wā (T) o te pendulum mēnā e whā ngā whakarea o te roa o te taura (l) i te roa tīmatanga.
Rongoā:
Te wā o te pendulum tuatahi:
Te roa tīmatanga o te taura:
Mena ka whakanuia te roa o te taura kia whā ngā wā i te roa tīmatanga:
Kātahi ko te wā o te pendulum:
Ko te roa o te nekehanga he 4 hēkona.
Ko te whakautu tika ko D.
3. E rua ngā pendulum he rite te roa o tō rāua taura, engari ko te taumaha o te pendulum tuarua e whā ngā wā te taumaha o te pendulum tuatahi. Mena ko f 1 te auau o te pendulum tuatahi, ā, ko f 2 te auau o te pendulum tuarua, whakatauhia te whanaungatanga i waenga i te f 1 me te f 2.
A. f 1 = f 2
B. f 1 = 2 f 2
C. f 2 = 2 f 1
D. f 1 = 4 f 2
Rongoā:
Te whārite o te auau o te pendulum māmā:
f = auau, g = whakaterenga nā te kaha ā-papa, l = te roa o te taura
I runga i te whārite i runga ake nei, ka taea e tātou te whakatau kāore te papatipu e pā ki te auau o te pendulum māmā.
Ko te whakautu tika ko A.
4. Ko ngā rahinga i raro nei kāore e pā ki te wā o te pendulum māmā ko…
A. te roa o te taura me te papatipu o te mea
B. te roa o te taura me te whakaterenga nā te kaha ā-papatipu
C. te papatipu o te mea me te koki tīmatanga
D. te roa o te taura me te koki tīmatanga
Rongoā:
Ko te whārite o te wā o te pendulum māmā:
T = wā, g = whakaterenga nā te kaha ā-papa, l = roa o te taura
I runga i te tātai i runga ake nei, ka taea te whakatau ko te roa o te tokotoko (l) me te whakaterenga o te kaha ā-papa (g) ka pā ki te wā o te pendulum māmā . Ki te kore, kāore te papatipu o te mea me te koki tīmatanga e pā ki te wā o te pendulum māmā m.
Ko te whakautu tika ko C.
5. He mea hanga te taura o te pendulum māmā ki te nairona. Kei tetahi pito o te taura he taumaha 10 karamu te taumaha, ā, ko te roa o te taura he 1 mita. Mena he rua te auau i te auau tuatahi, me whakarerekē te roa o te taura ki…
A. 0.25 mita
B. 0.50 mita
C. 2.0 mita
D. 4.0 mita
Mōhiotia:
Kāore te papatipu e pā ki te auau o te pendulum māmā.
Ko te roa o te taura o te pendulum māmā (l) = 1 mita
E hiahiatia ana: whakatauria te roa o te taura mēnā he rua te auau o te auau tīmatanga
Rongoā:
Ko te auau tīmatanga o te pendulum māmā:
Ko te auau o te pendulum māmā he rua te auau tīmatanga:
Kia takiruatia ai te auau whakamutunga , me whakarerekē te roa o te pendulum ki te 0.25 mita.
Ko te whakautu tika ko A.
