A mass hung on a spring oscillates with period

PHYSICS · Subjective · Fermi University Physics · Scientific Practice & Experimental Methods · Uncertainty in measurement · Data analysis and model fitting in the laboratory

Measurement and Method, Ch Graphs, straight lines and least squares

Problem

A mass

M

hung on a spring oscillates with period

T=2\pi\sqrt{(M+m_{\rm s})/k}

, where

k

is the spring constant and

m_{\rm s}

is an effective mass contributed by the spring itself. The period is timed for six hanging masses, each period with standard uncertainty

u(T)=0.004\,\mathrm{s}

. Choose the quantity to plot on each axis so that the relation becomes a straight line

Y=mX+c_0

, and state what the slope and the intercept each measure. The least-squares line through the six points has slope

m=3.95\,\mathrm{s^2\,kg^{-1}}

and intercept

c_0=0.079\,\mathrm{s^2}

. Find

k

and

m_{\rm s}

. One point has

T=(0.800\pm0.004)\,\mathrm{s}

. What value, and what vertical error bar, does it carry on your plot?

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