A block of mass attached to a horizontal spring with spring constant moves without…

MATHEMATICS · Single correct · AP · Calculus AB · Differential Equations · Differential Equations

Problem

A block of mass mm attached to a horizontal spring with spring constant kk moves without friction along a straight track. Let x(t)x(t) denote the block’s displacement from the spring’s natural (unstretched) length, measured positive to the right. Which of the following differential equations best models the block’s motion? (a) d2xdt2+2kmx=0\displaystyle \frac{d^{2}x}{dt^{2}}+\frac{2k}{m}x=0 (b) d2xdt2−kmx=0\displaystyle \frac{d^{2}x}{dt^{2}}-\frac{k}{m}x=0 (c) d2xdt2+kmx=0\displaystyle \frac{d^{2}x}{dt^{2}}+\frac{k}{m}x=0 (d) d2xdt2+k2mx=0\displaystyle \frac{d^{2}x}{dt^{2}}+\frac{k}{2m}x=0

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