A076416 Decimal expansion of third solution of equation cos(x)*cosh(x) = 1.

1, 0, 9, 9, 5, 6, 0, 7, 8, 3, 8, 0, 0, 1, 6, 7, 0, 9, 0, 6, 6, 6, 9, 0, 3, 2, 5, 1, 9, 1, 0, 5, 8, 9, 2, 4, 1, 7, 5, 4, 2, 8, 0, 3, 0, 3, 0, 5, 7, 6, 3, 6, 1, 9, 9, 7, 0, 7, 6, 5, 5, 5, 9, 0, 2, 6, 5, 6, 9, 2, 2, 8, 2, 8, 9, 0, 0, 2, 8, 7, 1, 2, 0, 3, 7, 6, 1, 7, 8, 7, 6, 2, 0, 2, 3, 5, 3, 4, 9, 8, 2, 7, 7, 9, 9

Offset: 2

Author

Zak Seidov, Oct 10 2002

Keywords

• easy
• nonn
• cons

Comments

This is an equation related to a beam clumped at both ends: cos(x) cosh(x) = 1. The first three solutions are: 4.73 (A076414), 7.853 (A076415) and 10.9956 (this sequence).

Examples

			10.995607838001670906669...
		

Links

• Z. Guede and I. Elishakov, A fifth-order polynomial that serves as both buckling and vibration mode of an inhomogeneous structure, Chaos, Solitons and Fractals 12 (7) (2001) 1267-1298.

Crossrefs

Cf. A076414, A076415.

Programs

Mathematica

RealDigits[x/.FindRoot[Cos[x] Cosh[x]==1,{x,7 Pi/2},WorkingPrecision -> 120]][[1]] (* Jean-François Alcover, Mar 14 2011 *)

PARI

solve(x=9,11,cos(x)*cosh(x)-1) \\ Charles R Greathouse IV, Mar 15 2011

Extensions

Offset corrected by R. J. Mathar, Feb 05 2009