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It's your turn on harmonic motion

solutions to the exercises

Do your best in trying to solve the following problems. In any case some of them are solved in the video and all of them are solved in the pdf file below.

Exercise 1.

Determine the amplitude, the period, the frequency and the phase of the harmonic motion represented by the function [xmapsto 2sin(3x+4)+3sin(3x-2).]

Exercise 2.

Determine the amplitude, the period, the frequency and the phase of the harmonic motion represented by the function [xmapsto 2sin(2x-frac pi 6)+frac 34cos(2x+frac{2pi}3).]

Exercise 3.

John’s blood pressure is modeled by the function [p:tmapsto 115+25sin(160pi t)] where (t) is the time measured in minutes.

1. Find the period of (p);

2. Find the number of heartbeats per minute;

3. Graph the function (p);

4. Compute the maximum and the minimum blood pressures.

Exercise 4.

Graph the functions (f:xmapsto x^2), (g:xmapsto -x^2), and (h:xmapsto x^2cos(6pi x)).