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(B) Let $M$ be the mass of the box and $m$ be the mass of the oscillating object. The scale measures the normal force $N$ exerted by the box on the sc

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At its minimum height

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(B) Let $M$ be the mass of the box and $m$ be the mass of the oscillating object. The scale measures the normal force $N$ exerted by the box on the scale. For the whole system (box + spring + mass),the forces acting are the weight $(M+m)g$ downwards and the normal force $N$ upwards. From Newton's second law for the mass $m$,the force exerted by the spring on the mass is $F_s = m(g + a)$,where $a$ is the acceleration of the mass (upward is positive). By Newton's third law,the mass exerts an equal and opposite force $F_s$ on the spring,which is transmitted to the box. Thus,the total normal force $N$ on the scale is $N = Mg + F_s = Mg + m(g + a) = (M+m)g + ma$. The scale reading is largest when the acceleration $a$ is at its maximum positive value (upward). In simple harmonic motion,the acceleration is directed towards the equilibrium position. At the minimum height (lowest point),the restoring force is upward and maximum,so the acceleration $a$ is at its maximum positive value. Therefore,the scale reading is largest when the mass is at its minimum height.

$A$ mass hangs from a spring and oscillates vertically. The top end of the spring is attached to the top of a box,and the box is placed on a scale,as shown in the figure. The reading on the scale is largest when the mass is

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