In the special case of the undamped ( \ delta = 0 ) and undriven ( \ gamma = 0 ) Duffing equation, an exact solution can be obtained using Jacobi's elliptic functions.
22.
Consequently, the adjectives " hardening " and " softening " are used with respect to the Duffing equation in general, dependent on the values of \ beta ( and \ alpha ).
23.
Dick's first active involvement in crime, comes where the brothers choose to go cattle duffing ( stealing ), even though an offer of solid, honest work had been made with neighbour and friend, George Storefield.
24.
Even after making his first bogey in 43 holes on No . 2, and making another bogey on No . 4 by duffing a wedge from the fairway to fall two strokes back, Tway appeared to have control of the tournament.
25.
The five golf courses that he enjoys the most are Troon North in Phoenix, Pebble Beach and Half Moon Bay in California, and two others I can't remember now because while he was parring the hole, I was duffing my way down the right rough.
26.
This shows that the solutions to the forced and damped Duffing equation can be described in terms of the three parameters ( \ varepsilon, \ eta and \ sigma ) and two initial conditions ( i . e . for y ( t _ 0 ) and \ dot { y } ( t _ 0 ) ).
27.
And the conversations on board and at the station _ hushed, as if already on the green on the first hole _ tended toward the lofty, from the uncommon joys of duffing across Scotland to the high cost of a corporate event attended the night before by a well-heeled, hung-over fan in his 20s.
28.
I am convinced that this led many to the conclusion on non-notability-after all who cares what a lot o'duffing Harry Potter fanatics might come up with in their imaginations when they should be outside playing football or something . " " Created a timeline " " suggested these crazy folks made it up out of thin air-thus original research . " " For the HP series . . . " " carried a tone that " we " ( or they the fans ) were doing this effort as a favor to assist Rowling and the world-suggesting'cruft . The fact that the detailed dates presented were derived from " " three shreds of information " " strongly suggested a lot of synthesis from less than solid information.
