Elements of Natural Philosophy, Volume 1 |
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Page 22
... equal , but the amplitude of one of them much greater than that of the other . To find the time and the amount of the maximum acceleration or retardation of phase , let CA be equal to the greater half - amplitude . From A as centre ...
... equal , but the amplitude of one of them much greater than that of the other . To find the time and the amount of the maximum acceleration or retardation of phase , let CA be equal to the greater half - amplitude . From A as centre ...
Page 23
... equal amplitudes in the two given motions . If their periods are equal , their resultant is a simple harmonic motion , whose phase is at every instant the mean of their phases , and whose amplitude is equal to twice the ampli- tude of ...
... equal amplitudes in the two given motions . If their periods are equal , their resultant is a simple harmonic motion , whose phase is at every instant the mean of their phases , and whose amplitude is equal to twice the ampli- tude of ...
Page 24
... equal areas described in equal times by the radius- vector from the centre ; although in particular cases it may be uniform circular , or , on the other hand , rectilineal and simple harmonic . 81. To prove this , we may first consider ...
... equal areas described in equal times by the radius- vector from the centre ; although in particular cases it may be uniform circular , or , on the other hand , rectilineal and simple harmonic . 81. To prove this , we may first consider ...
Page 25
... equal areas ( being the projections of the areas described by the radius of the circle ) in equal times . But the plane and position of the circle of which this projection is taken may clearly be found so as to fulfil the condition of ...
... equal areas ( being the projections of the areas described by the radius of the circle ) in equal times . But the plane and position of the circle of which this projection is taken may clearly be found so as to fulfil the condition of ...
Page 26
... equal areas are described by the radius - vector from the centre in equal times . Hence the proposition of § 80 . 84. We must next take the case of the composition of simple harmonic motions of different kinds and in different lines ...
... equal areas are described by the radius - vector from the centre in equal times . Hence the proposition of § 80 . 84. We must next take the case of the composition of simple harmonic motions of different kinds and in different lines ...
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Common terms and phrases
acceleration action amount angular velocity anticlastic attraction axis called centimetre centre of gravity centre of inertia circle circular co-ordinates component configuration consider constant cosine couple curvature curve cylinder denote density described diagram displacement distance ellipse ellipsoid elongation equal equations equilibrium external point finite fixed point flexure fluid forces acting friction geometrical given force Hence hodograph horizontal infinitely small instant inversely kinetic energy length magnitude mass matter measured moment of inertia momentum moving normal section P₁ P₂ parallel parallelogram of forces particle path pendulum perpendicular plane perpendicular portion position potential pressure principal axes principle produce projection proportional quantity radius radius of gyration reckoned rectangular right angles rigid body rotation round shear shell sides simple harmonic motion solid angle space spherical surface spiral square straight line strain stress suppose tangent theorem theory tion torsion uniform unit vertical whole wire