Trigonometric Function Modeling Spring Motion

The function, h(t ) = 6 cos(3π • t - $\frac{π}{3} $ ) + 4 , where h(t) is in metres and t is in seconds, models the movement
of a spinning wheel relative to the ground. Explain what is wrong with the equation.

1 Answer

Since $\cos (3\pi t -\frac{\pi}{3})$ takes the value $-1$ for  $3\pi t -\frac{\pi}{3}=(2k+1)\pi$. for such times

\[h(t)=6 (-1)+4=-2<0.\]

This means that at certain times the spring will be 2 meters underground! That's what is wrong with the equation

Erdos Erdos
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