Elements of Natural Philosophy, Volume 1 |
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Page 21
... expression used to designate the part of its whole period which it has reached . It is borrowed from the popular expression ' phases of the moon . ' Thus for Simple Harmonic Motion we may call the first or zero - phase that of passing ...
... expression used to designate the part of its whole period which it has reached . It is borrowed from the popular expression ' phases of the moon . ' Thus for Simple Harmonic Motion we may call the first or zero - phase that of passing ...
Page 25
... expression in Fourier's Theorem , to be presently enunciated . We give below a graphic representation of the composition of two simple harmonic motions in one line , of equal amplitudes and of periods which are as 1 : 2 and as 2 : 3 ...
... expression in Fourier's Theorem , to be presently enunciated . We give below a graphic representation of the composition of two simple harmonic motions in one line , of equal amplitudes and of periods which are as 1 : 2 and as 2 : 3 ...
Page 29
... expression , in mathematical language , for any arbitrary periodic function ; and consequently can express any function whatever between definite values of the variable 89. Any arbitrary periodic function whatever being given , the ...
... expression , in mathematical language , for any arbitrary periodic function ; and consequently can express any function whatever between definite values of the variable 89. Any arbitrary periodic function whatever being given , the ...
Page 30
... expressing a given arbitrary periodic function , -when once we are assured that the problem is possible ; and when we have this assurance , it proves that the reso- lution is determinate ; that is to say , that no other complex harmonic ...
... expressing a given arbitrary periodic function , -when once we are assured that the problem is possible ; and when we have this assurance , it proves that the reso- lution is determinate ; that is to say , that no other complex harmonic ...
Page 37
... expressing in two ways the area of the parallelogram IpOq , we have Hence Oq . IB = Op . Ia . Oq : Op :: w , w . .. In words , if on the axes OA , OB , we measure off from O lines Op , Oq , proportional respectively to the angular ...
... expressing in two ways the area of the parallelogram IpOq , we have Hence Oq . IB = Op . Ia . Oq : Op :: w , w . .. In words , if on the axes OA , OB , we measure off from O lines Op , Oq , proportional respectively to the angular ...
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Common terms and phrases
acceleration action amount angular velocity anticlastic attraction axis called centre of gravity centre of inertia circle circular co-ordinates component configuration consider constant cord corresponding 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 formulae friction geometrical given force Hence hodograph horizontal inclined infinitely small instant inversely kinetic energy length magnitude mass matter measured moment of inertia momentum moving normal section P₁ parallel particle path pendulum perpendicular plane perpendicular portion position 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 tion torsion uniform unit vertical weight whole wire