# Exercises for Chaos Under Control

## Chapter 6: Prisms, Pianos, and Spectral Analysis

1. The lower left graph shows the power spectrum of the
signal displayed in part (a) of that figure. Sketch the
power spectra of the signals shown in parts (b) and (c).
Answer

2. In the upper right graph we see the power
spectrum of the signal in (a). Sketch the signals for the power spectra
(b) and (c) shown in the figure.

3.[N] Suppose S_{1}(t) is a sine wave of amplitude 5 and period 60 seconds,
S_{2}(t) is a sine wave of amplitude 2 and period 30 seconds and
S_{3}(t) is a sine wave of amplitude 1 and period 20 seconds.
Suppose also that all three are zero at t = 0 and start to increase as t begins to
increase from 0. What is the amplitude of the composite wave
S_{1}(t) + S_{2}(t) + S_{3}(t) at

(a) t = 60 seconds, Answer

(b) t = 30 seconds, Answer

(c) t = 15 seconds. Answer

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