By Roof C. F.
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Extra resources for Dynamical Economics
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Comparisons of pitch. vibration of a free-free bar. Three nodes. Four nodes. Gravest mode Position of nodes. for clamped-free bar. Calculation Supported bar. of period for clamped-free bar from hypothetical type. Solution of problem for a bar with a loaded end. Effect of additions to a bar. Influence of irregularities of density. Correction for rotatory inertia. Boots of functions derived linearly from normal functions. Formation of equation of motion when there is permanent tension. Special ter minal conditions.
Pitches of the various simple tonea. Table of the roots of Bessol's functions. Nodal Figurou, Circular membrane with ono radius fixed. Effect of small load* Beasel's function** of fractional order. Vibrations of a membrane whoso boundary is approximately circular. In many cases tho pitch of a membrane may be calculated from the area alone* Of all membranes of equal avoa that of circular form has the gravest pitch. Pitch of a membrane whoso boundary is an in cases thai quencies m ellipse of small eccentricity.
Fixed rectangular bound in terms of normal co-ordinates. Normal V aud T equations of vibration. Examples of impressed forces. Frequency for an elongated rectangle depends mainly on the shorter side. Cases in which different modes of vibration have the same period. Derived modes thence arising. Effect of slight irregularities. An irregularity may remove mdeterminatenoss of normal mo Jos* Solutions applicable to a triangle. Expression of tho general differential equation by polar Of the two functions, which occur in the solution, one is excluded by the condition at the pole.