SAT Subject Physics Practice Question 59: Answer and Explanation

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Question: 59

6. A linear spring of force constant k is used in a physics lab experiment. A block of mass m is attached to the spring and the resulting frequency, f, of the simple harmonic oscillations is measured. Blocks of various masses are used in different trials, and in each case, the corresponding frequency is measured and recorded. If f2 is plotted versus 1/m, the graph will be a straight line with slope

A. 4π2/k2
B. 4π2/k
C. 4π2k
D. k/(4π2)
E. k2/(4π2)

Correct Answer: D


The frequency of a spring–block simple harmonic oscillator is given by the equation . Squaring both sides of this equation, we get f2 = Therefore, if f2 is plotted versus (1/m), then the graph will be a straight line with slope . (Note: The slope of the line whose equation is y = ax is a.)

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