To determine the interval during which the weight is above its resting position, we need to analyze the provided data for [tex]\( d(t) \)[/tex], the displacement in centimeters, at specific times [tex]\( t \)[/tex], measured in seconds.
The given table is:
[tex]\[
\begin{array}{|c|c|c|c|c|c|c|c|}
\hline
t & 0 & 0.015625 & 0.03125 & 0.046875 & 0.0625 & 0.078125 & 0.09375 \\
\hline
d(t) & -20 & -14.14 & 0 & 14.14 & 20 & 14.14 & 0 \\
\hline
\end{array}
\][/tex]
We want to find when [tex]\( d(t) > 0 \)[/tex]. Observing the values of [tex]\( d(t) \)[/tex] in the table:
1. [tex]\( t = 0: d(0) = -20 \)[/tex] (below equilibrium)
2. [tex]\( t = 0.015625: d(0.015625) = -14.14 \)[/tex] (below equilibrium)
3. [tex]\( t = 0.03125: d(0.03125) = 0 \)[/tex] (at equilibrium)
4. [tex]\( t = 0.046875: d(0.046875) = 14.14 \)[/tex] (above equilibrium)
5. [tex]\( t = 0.0625: d(0.0625) = 20 \)[/tex] (above equilibrium)
6. [tex]\( t = 0.078125: d(0.078125) = 14.14 \)[/tex] (above equilibrium)
7. [tex]\( t = 0.09375: d(0.09375) = 0 \)[/tex] (at equilibrium)
The weight is above its resting position (i.e., [tex]\( d(t) > 0 \)[/tex]) between the intervals of [tex]\( t \)[/tex]:
- Between [tex]\( 0.03125 \)[/tex] and [tex]\( 0.09375 \)[/tex].
From the options given, the correct interval would be:
D. [tex]\((0.03125, 0.09375)\)[/tex]
Thus, the correct answer is:
D. [tex]\((0.03125, 0.09375)\)[/tex]
