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This work is motivated by naval use of passive towed sonar arrays of hydrophones. We consider the simplest model of a towed mass. The mass is considered to move only in a horizontal direction x perpendicular to the tow direction. The tension in the tow cable is expected to be nonconstant due to turbulence, and is modeled by a sinusoidal forcing function. The resulting differential equations are analyzed for linear stability and nonlinear dynamical effects. In particular we study the nonlinear dynamics of the ODE: x ¨ + ( δ + ϵ cos t ) x + x ˙ | x ˙ | = 0

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We investigate the in-flight dynamics of a simplified model of a supercavitating body. In particular we are interested in the nature and frequency of the impacts which occur as the tail of the body touches the cavity walls. Referring to laboratory experiments conducted at Cal Tech in the 1950’s, we show that the tip force by the fluid is approximately directed along the length of the body. This gives zero moment about the body’s center of mass which leads us to assume that the body moves as if it were a moment-free rigid body pinned at its tip. To simplify the analysis, we assume that the body is not spinning about its symmetry axis. Then the motion between impacts is a plane motion with constant angular velocity. Using elementary fluid mechanics, we model the impact occurring when the tail touches the cavity walls, and we show that it is reasonable to assume that the impact is instantaneous with coefficient of restitution unity. Using this simplified model, we offer a simulation for typical parameters.