The mass m is supported on a thin inextensible wire stretched across the frame with tension T. (a) Show that if T = const and if y/L  1, then the force on the mass is given approximately by F =...

The mass m is supported on a thin inextensible wire stretched across the frame with tension T.

(a) Show that if T = const and if y/L
 1, then the force on the mass is given approximately by F = −(2y/L)T, and a bond graph for the system (neglecting the inertia of the frame) is

(b) When T is allowed to vary by connecting a force source to the wire, the equivalent spring seems to simply have a “variable constant.” This concept is not very profound, however, since a —C element must be conservative, and with variable T the relation between F_y
and y is not.

Show that if y/L
 1, the distance the end of the wire moves against the force source, δ, is δ = y²/L. Use this relation to show a bond graph that represents the effect of the wire by means of a force source and a displacement-modulated transformer. Note that this model shows a causal restriction that was not evident in the previous bond graph.