232 The UMAP Journal 24.3 (2003) where wn E C satisfies the dispersion relation n丌)2 Consider the lowest-order normal mode(n= 1). For F< Fcrit E T D/e we have w2>0 1∈卫, and the normal mode just oscillates in time, giving stable solutions. However, if F> Fcrit, then wl <0 and w=+iw, W ER, i.e. there are exponentially growing solutions(o eat), and the normal- mode solution becomes unstable. Thus, the box wall buckles for applied forces F>T2D/e2. The buckling force is D which is (2 References Bever, Michael B.(ed )1986. Encyclopedia of Materials Science and engineering Vol 2. Cambridge, MA: MIT Press Blaine, David. 2002. David Blaine's Vertigo. Television special, May 2002 EncyclopaediaBritannicaOnline.2003.http://search.eb.com/ Polking, John C. 2002. ODE Software for MATLAB. 4th order Runge-Kutta demonstrationrk4.m.http://math.riceedu/-dfield Resnick, robert, David Halliday, and Kenneth S. Krane. 1992. Physics. New York: John Wiley and Sons Thorne, Kip S, and Roger D. Blandford. 2002. Ph136 Applications of Classical physics. Unpublished lecture notes. Pasadena, CA: Califor- niaInstituteofTechnology.http://www.pma.caltech.edu/courses/pH136/ yr2002/index. html232 The UMAP Journal 24.3 (2003) where ωn ∈ C satisfies the dispersion relation ω2 n = 1 Λ nπ  2 nπ  2 D − F  . Consider the lowest-order normal mode (n = 1). For F <Fcrit ≡ π2D/2, we have ω2 1 > 0, so ω1 ∈ R, and the normal mode just oscillates in time, giving stable solutions. However, if F >Fcrit, then ω2 1 < 0 and ω = ±i,  ∈ R, i.e. there are exponentially growing solutions (∝ et), and the normal￾mode solution becomes unstable. Thus, the box wall buckles for applied forces F >π2D/2. The buckling force is FB = π2D 2 = Y π2 12 wt3 2 , which is (2). References Bever, Michael B. (ed.) 1986. Encyclopedia of Materials Science and Engineering. Vol. 2. Cambridge, MA: MIT Press. Blaine, David. 2002 . David Blaine’s Vertigo. Television special, May 2002. Encyclopaedia Britannica Online. 2003. http://search.eb.com/. Polking, John C. 2002. ODE Software for MATLAB. 4th order Runge-Kutta demonstration rk4.m. http://math.rice.edu/~dfield/ . Resnick, Robert, David Halliday, and Kenneth S. Krane. 1992. Physics. New York: John Wiley and Sons. Thorne, Kip S., and Roger D. Blandford. 2002. Ph136: Applications of Classical Physics. Unpublished lecture notes. Pasadena, CA: Califor￾nia Institute of Technology. http://www.pma.caltech.edu/Courses/ph136/ yr2002/index.html .