等速圓周運(yùn)動(dòng)與簡(jiǎn)諧運(yùn)動(dòng)shmsimpleharmonicmotion(編輯修改稿)
2024-08-17 04:33 本頁面
【文章內(nèi)容簡(jiǎn)介】 MLT322221231?? ??思考問題 :機(jī)械式傳統(tǒng)鐘錶通常皆依賴振動(dòng)系統(tǒng)來計(jì)時(shí)，為何振動(dòng)系統(tǒng)可為時(shí)間之標(biāo)準(zhǔn)。 扭擺 (Torsional Pendulum) 繩索因此角度扭轉(zhuǎn)而施予此物體一力矩，其大小與扭轉(zhuǎn)角度成正比，方向?yàn)闇p小此扭轉(zhuǎn)角度的方向。由此我們可以寫出此系統(tǒng)的運(yùn)動(dòng)方程 ????????? 22222???????? IdtddtdI ?? IT 2?所以，扭擺亦為一簡(jiǎn)諧運(yùn)動(dòng)。其頻率為 The otolith ans are the primary means by which we sense linear acceleration of the head and the orientation of the head with respect to Earth39。s gravity. Each of these otolith ans contains a small sensory area known as a macula. Each macula contains several thousand vestibular hair cells. The cilia are embedded in a gelatinous matrix called the otolithic membrane. This membrane contains small piles of calcium carbonate crystals (CaCO3), called otoliths, a word which literally means ear stones. 阻尼諧振子 (Damped Oscillators) 考慮一系統(tǒng)的阻力 (retarding force)為 R=bv，恢復(fù)力 (restoring force)為 kx，則由牛頓運(yùn)動(dòng)定律可得 ? ???????? 22dtxdmdtdxbkxmabvkxF 此運(yùn)動(dòng)方程與所熟悉的簡(jiǎn)諧運(yùn)動(dòng)微分方程差異於多出一次微分項(xiàng)。在此微分方程中，對(duì)函數(shù) x而言為齊次方程，故在解此類型的微分方程時(shí)，我們可以複數(shù)形式當(dāng)成微分方程一般解的形式。 tAex ??022 2222 ?????? xdtdxdtxdmbmkoo ???? 令 再將此一般解形式代入方程中可得特徵方程 0202 2222 ??????? oo xxx ???????? 首先將微分方程整理成 此特徵方程的兩個(gè)解為 tto eAeAx 21 21222,1?????? ??????? 過阻尼情況 (overdamped oscillator) 22o?? ?臨界阻尼情況 (critical damped oscillator) 22o?? ?阻尼不足情況(underdamped oscillator) 22o?? ?此時(shí)特徵方程的兩個(gè)解相等 ??? ???21tetAAx ???? )(21運(yùn)動(dòng)通解為一般解的實(shí)數(shù)部分 ? ?? ?titit eCeCex ??? ???? ?? 21Re臨界阻尼情況 (critical damped oscillator) 22o?? ?阻尼不足情況
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