Elements of Natural Philosophy, Part 1 |
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Page 24
Investigation regarding complex harmonic functions has led to results of the
highest importance , having their most general ... We give below a graphic
representation of the composition of two simple harmonic motions in one line , of
equal ...
Investigation regarding complex harmonic functions has led to results of the
highest importance , having their most general ... We give below a graphic
representation of the composition of two simple harmonic motions in one line , of
equal ...
Page 25
The given motion A of P in BA will be ( § 67 ) defined by the motion of a point Q
round the circumference PH of this circle ; and the same point , if moving in the
direction indicated by the arrow , will B IO P give a simple harmonic motion of P ' ,
in ...
The given motion A of P in BA will be ( § 67 ) defined by the motion of a point Q
round the circumference PH of this circle ; and the same point , if moving in the
direction indicated by the arrow , will B IO P give a simple harmonic motion of P ' ,
in ...
Page 26
We must next take the case of the composition of simple harmonic motions of
different kinds and in different lines . In general , whether these lines be in one
plane or not , the line of motion returns into itself if the periods are
commensurable ...
We must next take the case of the composition of simple harmonic motions of
different kinds and in different lines . In general , whether these lines be in one
plane or not , the line of motion returns into itself if the periods are
commensurable ...
Page 27
Another very important case is that of two groups of two simple harmonic motions
in one plane , such that the resultant of each group is uniform circular motion . If
their periods are equal , we have a case belonging to those already treated ...
Another very important case is that of two groups of two simple harmonic motions
in one plane , such that the resultant of each group is uniform circular motion . If
their periods are equal , we have a case belonging to those already treated ...
Page 28
Before leaving for a time the subject of the composition of harmonic motions , we
must enunciate Fourier's Theorem , which is not only one of the most beautiful
results of modern analysis , but may be said to furnish an indispensable
instrument ...
Before leaving for a time the subject of the composition of harmonic motions , we
must enunciate Fourier's Theorem , which is not only one of the most beautiful
results of modern analysis , but may be said to furnish an indispensable
instrument ...
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acceleration according acting action amount angle angular applied attraction axes axis body called centre centre of inertia circle component condition consider constant corresponding couple course curvature curve denote density described determined direction displacement distance divided effect elastic elements energy equal equations equilibrium evidently experience expression figure fixed fluid force friction give given gravity harmonic Hence important increase infinitely small instant interval kinetic length less mass matter mean measured method motion moving natural normal observation opposite parallel particle passing path perpendicular plane portion position potential practical pressure principle problem produce projection proportional quantity radius reference relative remain respectively rest resultant right angles rigid rotation round sides simple solid space spherical square straight strain stress suppose surface theory turned uniform unit velocity weight whole wire