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Analysis of a flexible beam with displaced end-located inertial masses is presented. The resulting three-dimensional mode shape is shown to consist of two one-plane bending modes and one torsional mode. These three components of the mode shapes are shown to be linear combinations of trigonometric and hyperbolic sine and cosine functions. Boundary conditions are derived to obtain nonlinear algebraic equations through kinematic coupling of the general solutions of the three governing partial differential equations. A method of solution which takes these boundary conditions into account is also presented. A computer program has been written to obtain unique solutions to the resulting nonlinear algebraic equations. This program, which calculates natural frequencies and three-dimensional mode shapes for any number of modes, is presented and discussed.

1Futility, Or the Wreck of the Titan

By Morgan Robertson

This novel was published a full 14 years before the sinking of the Titanic, but listeners may be surprised at how many parallels this fictional tale has with subsequent true events.<br /><br />The Titan is the largest and most technologically advanced steamship of her time. She is considered unsinkable. Her full speed crossings of the Northern Lane Route carry her rich passengers in the highest standards of luxury and comfort. The less well-off travel in rougher quarters but still benefit from the speed of travel. These crossings, however, are fraught with navigational hazards, the greatest of which is ice.<br /><br />Unlike the ship, one member of her crew is not of the highest standard. At least, not anymore. John Rowland is a broken man who drinks to forget his past. However, when the Titan crashes into an iceberg during her attempt to break a speed record, he is forced to confront his past. Can he overcome his enemies and escape as the ship begins to sink? And can he make his way back to civilization and find self-respect once more? Adventure and soul-searching await Rowland, with a surprise ending.

2Aids to Forensic Medicine and Toxicology

By W. G. Aitchison Robertson

A 1922 source-book for British criminal pathologists, this will be of particular interest to fans of popular police forensics television shows, films, and murder mysteries.(Summary by BellonaTimes)

A dozen men jailbreak from a naval prison, and steal the newest destroyer tied up at the docks to escape in: the fastest ship in the navy. However a young officer was the only one on board, and is now a part of the voyage to escape. Things get tense when he awakens, and finds his boyhood rival and enemy is one of the jailbreakers on board! Can the officer find a way to sabotage their escape, without being thrown overboard himself? - Summary by Joe DeNoia

4Wreck of the Titan, or Futility

By Morgan Robertson

The Titan: the latest and most awesome industrial feat of modern luxury ocean liner, holding two thousand passengers, is set to sail the Northern Lane Route between New York and England. This alleged unsinkable and indestructible vessel is set to beat the record for this voyage in less than 5 days! In her crew: John Rowland; a drunk, and washed-out naval seaman. On the passenger list: Myra Selfridge, and her little daughter. A former lover who wants nothing to do with Rowland, due to his drinking. After a collision with an Iceberg and all hands deemed lost, Rowland finds himself fighting for life on an ice floe...and in his charge: keeping alive Myra's little daughter! (This novella was written 14 years before the Titanic set sail) - Summary by Joe DeNoia