A triangular shaped component is drawn by connecting points O (0,0), the origin of the system of coordinates with A (0, 24) and B (7.2, 0). Assume all dimensions in cm and that the plate is cut from a material of a density p = 0.079kg/cm. The project is an experiment to compare the period of oscillations if the triangular part is left to freely oscillated about an axis that is perpendicular to the plate through points A and B respectively. Study the case and calculate

Elements Of Electromagnetics
7th Edition
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Author:Sadiku, Matthew N. O.
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A triangular shaped component is drawn by connecting points O (0,0), the
origin of the system of coordinates with A (0, 24) and B (7.2, 0). Assume all
dimensions in cm and that the plate is cut from a material of a density
p = 0.079kg/cm². The project is an experiment to compare the period of
ocillations if the triangular part is left to freely oscillated about an axis that is
perpendicular to the plate through points A and B respectively. Study the
case and calculate
The mass of the plate :
kg.
The mass moment of inertia about the horizontal xx - axis (passing through O
and B) is: Ixx =
kg cm?
The mass moment of inertia about the vertical yy - axis (passing through O
and A): Iyy =
kg cm
Ixx and I yy calculated above can be combined using the
axes theorem to calculate the I, =
kg cm2 the moment of Inertia about the z-axis (normal to the plane through
O).
Consider the center of gravity of the triangular shape G. The moment of
Inertia IG-zz through an axis that is perpendicular to the plane through G can
* axes theorem resulting
be obtained from I2, using the
into IG-zz =
kg cm2
Calculate the moment of inertia IA-zz about the perpendicular to the plane
passing though point A: IA-zz
kgcm2 and the applicable
radius of inertia k A
cm The period of oscillations about A is
%3D
S
Transcribed Image Text:A triangular shaped component is drawn by connecting points O (0,0), the origin of the system of coordinates with A (0, 24) and B (7.2, 0). Assume all dimensions in cm and that the plate is cut from a material of a density p = 0.079kg/cm². The project is an experiment to compare the period of ocillations if the triangular part is left to freely oscillated about an axis that is perpendicular to the plate through points A and B respectively. Study the case and calculate The mass of the plate : kg. The mass moment of inertia about the horizontal xx - axis (passing through O and B) is: Ixx = kg cm? The mass moment of inertia about the vertical yy - axis (passing through O and A): Iyy = kg cm Ixx and I yy calculated above can be combined using the axes theorem to calculate the I, = kg cm2 the moment of Inertia about the z-axis (normal to the plane through O). Consider the center of gravity of the triangular shape G. The moment of Inertia IG-zz through an axis that is perpendicular to the plane through G can * axes theorem resulting be obtained from I2, using the into IG-zz = kg cm2 Calculate the moment of inertia IA-zz about the perpendicular to the plane passing though point A: IA-zz kgcm2 and the applicable radius of inertia k A cm The period of oscillations about A is %3D S
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