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Category: Mechanics

Question-213234

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Question Number 213234 by ajfour last updated on 01/Nov/24 Commented by Ghisom last updated on 01/Nov/24 $$\mathrm{let}\:{r}=\mathrm{1} \\ $$$${P}\in\mathrm{circle}:\:{P}=\begin{pmatrix}{\mathrm{cos}\:\theta}\\{\mathrm{1}+\mathrm{sin}\:\theta}\end{pmatrix} \\ $$$$\mathrm{parabola}:\:{y}=\left(\frac{\mathrm{2}+\mathrm{sin}\:\theta}{\mathrm{cos}\:\theta}−\frac{{x}}{\mathrm{cos}^{\mathrm{2}} \:\theta}\right){x} \\ $$$$\mathrm{tan}\:\alpha=\frac{\mathrm{2}+\mathrm{sin}\:\theta}{\mathrm{cos}\:\theta} \\…

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Consider-a-system-consisting-ofw-to-masses-m-1-and-m-2-where-the-pendulum-rod-has-an-nolinear-elastic-coefficient-k-k-0-1-2-with-being-the-angle-between-the-rodand-the-vertical-directi

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Question Number 211677 by MrGaster last updated on 16/Sep/24 $$\mathrm{Consider}\:\mathrm{a}\:\mathrm{system}\:\mathrm{consisting}\:\mathrm{ofw} \\ $$$$\mathrm{to}\:\mathrm{masses}.\boldsymbol{{m}}_{\mathrm{1}} \boldsymbol{\mathrm{and}}\:\boldsymbol{{m}}_{\mathrm{2}} ,\mathrm{where}\:\mathrm{the}\:\mathrm{pendulum}\:\mathrm{rod}\:\mathrm{has}\:\mathrm{an} \\ $$$$\mathrm{nolinear}\:\mathrm{elastic}\:\mathrm{coefficient}\:\boldsymbol{{k}}\left(\boldsymbol{\theta}\right)=\boldsymbol{{k}}_{\mathrm{0}} \left(\mathrm{1}+\boldsymbol{\alpha\theta}^{\mathrm{2}} \right),\mathrm{with}\boldsymbol{\theta}\:\mathrm{being}\:\mathrm{the}\:\mathrm{angle}\:\mathrm{between}\:\mathrm{the}\: \\ $$$$\mathrm{rodand}\:\mathrm{the}\:\mathrm{vertical}\:\mathrm{direction}. \\ $$$$\mathrm{Suppose}\:\mathrm{the}\:\mathrm{angle}\:\mathrm{is}\:\mathrm{smallh} \\ $$$$\mathrm{enoug}\:\mathrm{that}\:\boldsymbol{\theta}\:\mathrm{The}\:\mathrm{square}\:\mathrm{of}\:\mathrm{can}\:\mathrm{be}\:\mathrm{ignored}\: \\…

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