Question

A. y = 12 cos (12)B. y = cos (1) +12C. y = 12 cos (2x) + 12OD. y = 12 coB (-) +12

Answer 1

To solve this question, we need to visualize the wheel. See below:

The motion f the pot is clearly a cosine motion, the minimum height is 0 instead of -12, so we can see that the cosine function has been shifted up by 12 units, so our equation is;

$\begin{gathered} y=a\cos kx+12 \\ a\text{ is the amplitude of the height of the point above the centre only, so a =12} \\ y=12\cos kx+12 \\ k=\frac{2\pi}{\lambda} \\ \lambda=2\times\pi\times12=24\pi \\ so,k=\frac{2\pi}{24\pi}=\frac{1}{12} \\ \end{gathered}$

Thus, the complete equation is;

$y=12\cos (\frac{1}{12}x)+12$

That is Option D