QUESTION

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1. An oscillator is made from a block of mass $m$ and a series-parallel combination of linear springs. The oscillator is attached to a ceiling as shown in the figure. The springs are of two types that have spring constants $k_{1}$ and $k_{2}$ where $k_{2}=2 k_{1}$. The block is displaced downward a distance $y$ and released. Which of the following is a correct Newton's second law equation for the motion of this oscillator? (A) $\frac{d^{2} y}{d t^{2}}=-\frac{3}{4} \frac{k_{1}}{m} y$ (B) $\frac{d^{2} y}{d t^{2}}=-\frac{4}{3} \frac{m}{k_{1} y}$ (C) $\frac{d^{2} y}{d t^{2}}=-4 \frac{k_{1}}{m} y$ (D) $\frac{d^{2} y}{d t^{2}}=-3 \frac{k_{1}}{m} y$ (E) $\frac{d^{2} y}{d t^{2}}=-\frac{2}{5} \frac{k_{1}}{m} y$

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