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The axis of rotation, the axle of the physical pendulum is parallel to the axis of rotation, the axle of the lever. The axle bed of the lever is connected to the surface with girders. The axle of the physical pendulum is oscillating up and down, when the pendulum is out of balance.

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The restoring force on a pendulum is caused by gravity. Incidentally, because of the pendulum’s own inertia, you will see that the mass of the pendulum cancels out of the equations, and the period of a pendulum is independent of mass. As gravity points down, we need to take the component of gravity which is parallel to its motion.

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As best shown in FIG. 1, the presently preferred embodiment of apparatus 10 broadly includes a compound physical pendulum 12 operatively associated with a pressure control servovalve, generally indicated at 13; a cylindrical flywheel or inertia wheel 14 mounted on the vehicle 11 for rotation about a horizontal axis parallel to the longitudinal ...

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The period of oscillation for the physical pendulum will then be given by: 1 T = 211 mgh Note: - when calculating the momentum of inertia of a rigid body a useful relationship is the parallel – axis theorem: 1 = Icm + mh? parallel to OC.Thatis,fis the control input that acts directly on the mass m. In order to describe the pendulum motion, the origin of the inertial frame is chosen at point O.Thex-axis and y-axis are set in the horizontal and vertical directions, respectively. Let the generalized coordinates be denoted by a two-dimensional vector q: r,θ T where r

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Physical Pendulum [θ(t)=θmaxCos(ωt+φ)] ω = √mgh/I; T = 2π/ω = 2π√I/mgh I is the rotational inertia about the pivot point May require use of Parallel Axis Theorem to determine this h is the distance from the center of mass to the pivot point Note that T→∞ when h→0; a pendulum will not oscillate if the

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This is called the parallel axis theorem given by [latex] {I}_{\text{parallel-axis}}={I}_{\text{center of mass}}+m{d}^{2} [/latex], where d is the distance from the initial axis to the parallel axis. Moment of inertia for a compound object is simply the sum of the moments of inertia for each individual object that makes up the compound object.

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