Natural Frequencies

The questions below are due on Friday September 13, 2024; 05:00:00 PM.

You are not logged in.
Please Log In for full access to the web site.
Note that this link will take you to an external site (https://shimmer.mit.edu) to authenticate, and then you will be redirected back to this page.

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 <