File Name: conical pendulum problems and solutions .zip
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The conical pendulum lab allows students to investigate the physics and mathematics of uniform circular motion. The plane and the supporting string trace a conical pendulum. Students measure the velocity of the plane directly and then compare that value to the velocity predicted by analyzing the forces acting on the plane. Make sure the plane is mounted securely and will not break loose during flight. First, check that the battery compartment of the plane is securely fastened. Ensure that no one is in the path of the plane. Wear safety glasses to prevent eye injury.
6.7: Problems and Solutions
In this article, we consider the behaviour of a simple undamped spherical pendulum subject to high-frequency small amplitude vertical oscillations of its pivot. We use the method of multiple scales to derive an autonomous ordinary differential equation describing the slow time behaviour of the polar angle which generalises the Kapitza equation for the plane problem. We analyse the phase plane structure of this equation and show that for a range of parameter values there are conical orbits which lie entirely above the horizontal. Going further, we identify a family of quasi-conical orbits some of which may lie entirely above the pivot and establish that initial conditions can be chosen so that precession is eliminated for these orbits. For the general initial value problem, we show that the leading order solutions for the polar and azimuthal angles diverge significantly from their exact counterparts. However, by consolidating the slow scale error term into the leading order structure we may construct extremely accurate solutions for the slow scale evolution of the system.
Consider a conical pendulum with a mass m, attached to a string of length L. The mass executes uniform circular motion in the horizontal plane.
The nonlinear dynamic behavior of liquid sloshing in a carrier is investigated in this research with consideration the effects of viscosity of the liquid and varying gravity on the carrier. Liquid sloshing in the tank of the carrier is analogized as a three-dimensional nonlinear conical pendulum model. The solutions of the coupled governing equations for the sloshing are developed and solved numerically. Both inviscid and viscous liquids are considered and compared for their effects on the sloshing.
A pendulum is a body suspended from a fixed support so that it swings freely back and forth under the influence of gravity. When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position. When released, the restoring force acting on the pendulum's mass causes it to oscillate about the equilibrium position, swinging it back and forth. The mathematics of pendulums are in general quite complicated. Simplifying assumptions can be made, which in the case of a simple pendulum allow the equations of motion to be solved analytically for small-angle oscillations.
In this case, the string makes a constant angle with the vertical. The bob of pendulum describes a horizontal circle and the string describes a cone. Expression for Period of Conical Pendulum:. The time taken by the bob of a conical pendulum to complete one horizontal circle is called the time period of the conical pendulum. Expression for Tension in the String of Conical Pendulum:. A simple pendulum is a special case of a conical pendulum in which angle made by the string with vertical is zero i.
A conical pendulum consists of a weight or bob fixed on the end of a string or rod suspended from a pivot. Its construction is similar to an ordinary pendulum ; however, instead of swinging back and forth, the bob of a conical pendulum moves at a constant speed in a circle with the string or rod tracing out a cone. The conical pendulum was first studied by the English scientist Robert Hooke around  as a model for the orbital motion of planets.