A particle oscillates along the x-axis according to x=sin²(t/2), with x₀=1. Which graph correctly represents kinetic energy K versus position x?
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A particle oscillates along the x-axis according to x=sin²(t/2), with x₀=1. Which graph correctly represents kinetic energy K versus position x?

G1 Physics · Accepted Answer

x=sin²(t/2)=(1-cos t)/2, so x-1/2=-(cos t)/2. Thus the motion is SHM about x=1/2 with amplitude 1/2. In SHM, K∝A²-(x- x m e a n ) 2 , x_mean)², x m ​ e an ) 2 , a downward parabola: K=0 at x=0,1 and maximum at x=1/2. This is graph (3).