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(D) The period of oscillation $T$ for a spring-mass system is given by $T = 2\pi \sqrt{\frac{M_{total}}{K}}$,where $M_{total} = M + m_p$ ($M$ is the a

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Mass of the pan was neglected

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(D) The period of oscillation $T$ for a spring-mass system is given by $T = 2\pi \sqrt{\frac{M_{total}}{K}}$,where $M_{total} = M + m_p$ ($M$ is the added mass and $m_p$ is the mass of the pan).Squaring both sides,we get $T^2 = \frac{4\pi^2}{K} (M + m_p) = \frac{4\pi^2}{K} M + \frac{4\pi^2 m_p}{K}$.This equation is of the form $y = mx + c$,where $y = T^2$ and $x = M$.The intercept on the $T^2$ axis is $c = \frac{4\pi^2 m_p}{K}$.If the mass of the pan $m_p$ were zero,the graph would pass through the origin. Since the graph does not pass through the origin,it indicates that the mass of the pan was not accounted for (neglected) in the calculation of the total mass.

The graph shown was obtained from experimental measurements of the period of oscillations $T$ for different masses $M$ placed in the scale pan on the lower end of the spring balance. The most likely reason for the line not passing through the origin is that the

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