Question 1197680
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Find the trigonometric model for a simple harmonic motion that has initial displacement of 0 
at t=0, and amplitude of 5 inches, and a frequency 4/3 cycles per second 
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<pre>
The frequency is  4/3 per second.  It means that the period is 3/4 of a second.


The problem says NOTHING about the phase shift.


It only says that the initial displacement is 0 (zero).


There are TWO harmonic (sinusoidal) models satisfying the imposed conditions.


One model is  y = {{{5*sin(((2*pi)/((3/4)))*t))}}} = {{{5*sin(((8*pi)/3)*t))}}}.


Another model is y = {{{-5*sin(((8*pi)/3)*t))}}}.


Both models have zero displacements at t= 0.
</pre>

Solved.


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The lesson to learn from my solution is that there are TWO different models 
(different geometrically and physically) satisfying the imposed conditions.


These models are shifted half-period one from the other.


@Theo missed one of them.



It is, of course, the major intention of this problem for the student to find BOTH harmonics.



I would like to add something at the end.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It is good if you have formal knowledge of a subject.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;But in many cases it is not enough to solve problems correctly.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;In addition to formal knowledge, you should have adequate physical and geometrical intuition,

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;which is the same as common sense.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The problems like this one help you to develop such intuition and common sense. 

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It is the major benefit of solving such problems.