# 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 *f*^{2} is plotted versus 1/*m*, the graph will be a straight line with slope

A. 4π^{2}/*k*^{2}

B. 4π^{2}/*k*

C. 4π^{2}*k*

D. *k*/(4π^{2})

E. *k*^{2}/(4π^{2})

**Correct Answer:** D

**Explanation:**

The frequency of a spring–block simple harmonic oscillator is given by the equation . Squaring both sides of this equation, we get *f*^{2} = Therefore, if *f*^{2} 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*.)