Natural Frequencies

The questions below are due on Friday February 14, 2025; 10:00:00 AM.
 
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For the following problems, assume that y[n] = \alpha_1 y[n-1] and consider the following stem plots of the sequence y[n].

If the answer is a single plot, enter the letter of that plot. If the answer includes multiple plots, enter the letters of those plots in sequence: i.e., to select plots A and B enter AB.

For which plots above is \alpha_1 > 0?

For which plots above is |\alpha_1| < 1?

For which plots above is \alpha_1 < -1?

For which plots above is \alpha_1 > 1?

Suppose that y[0] = 1. For what range of positive values of \alpha_1 could 1\ge y[100] > 0.9?

\alpha_1 \le
\alpha_1 >

Suppose that y[0] = 1. For what range of positive values of \alpha_1 could 1\le y[100] < 1.1?

\alpha_1 \ge
\alpha_1 <