【摘要】：教學(xué)經(jīng)常使用固有頻率表達(dá)式不顯含彈簧靜變形和重力加速度的振子;但也能找到相反的情形.本研究探討前者的充要條件.分析發(fā)現(xiàn)如果彈簧軸線在質(zhì)點(diǎn)通過(guò)靜平衡位置時(shí)沿其軌跡的切向,則彈簧靜變形從固有頻率表達(dá)式中消失.在滿足這一前提下,進(jìn)一步要求質(zhì)點(diǎn)軌跡在靜平衡位置的曲率為0,或沿鉛垂方向,則重力也無(wú)回復(fù)力的效果,從而重力加速度在固有頻率表達(dá)式中不出現(xiàn).該結(jié)論不僅有助于理解重力與固有頻率之間的關(guān)系,也可指導(dǎo)振動(dòng)例題編制和選用.
[Abstract]:Natural frequency expressions are often used in teaching not to show oscillators with spring static deformation and gravity acceleration, but the opposite can also be found. This paper discusses the necessary and sufficient conditions of the former. It is found that the spring static deformation disappears from the natural frequency expression if the spring axis follows the tangential direction of the trajectory when the particle passes through the static equilibrium position. Under this premise, the curvature of the particle trajectory in the static equilibrium position is further required to be 0, or along the vertical direction, then gravity has no effect of restoring force, so that the acceleration of gravity does not appear in the expression of natural frequency. This conclusion is helpful not only to understand the relationship between gravity and natural frequency, but also to guide the compilation and selection of vibration examples.
【作者單位】： 中國(guó)農(nóng)業(yè)大學(xué)理學(xué)院;北京聯(lián)合大學(xué)應(yīng)用文理學(xué)院;
【基金】：北京市屬高等學(xué)校高層次人才引進(jìn)與培養(yǎng)計(jì)劃項(xiàng)目(CIT&TCD201404080)資助
【分類號(hào)】：O314-4;G642
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本文編號(hào)：2458806