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The kinetic energy of the system is: = (˙ + ˙) where is the mass of the bobs, is the length of the strings, and , are the angular displacements of the two bobs from equilibrium. The potential energy of the system is: E p = m g L ( 2 − cos θ 1 − cos θ 2 ) + 1 2 k L 2 ( θ 2 − θ 1 ) 2 {\displaystyle E_{\text{p}}=mgL(2-\cos ...
The pendulum reaches greatest kinetic energy and least potential energy when in the vertical position, because it will have the greatest speed and be nearest the Earth at this point. On the other hand, it will have its least kinetic energy and greatest potential energy at the extreme positions of its swing, because it has zero speed and is ...
Kinetic energy T is the energy of the system's motion and is a function only of the velocities v k, not the positions r k, nor time t, so T = T(v 1, v 2, ...). V , the potential energy of the system, reflects the energy of interaction between the particles, i.e. how much energy any one particle has due to all the others, together with any ...
The Q is equal to 2π times the energy stored in the pendulum, divided by the energy lost to friction during each oscillation period, which is the same as the energy added by the escapement each period. It can be seen that the smaller the fraction of the pendulum's energy that is lost to friction, the less energy needs to be added, the less the ...
which illustrates the kinetic energy is in general a function of the generalized velocities, coordinates, and time if the constraints also vary with time, so T = T(q, dq/dt, t). In the case the constraints on the particles are time-independent, then all partial derivatives with respect to time are zero, and the kinetic energy is a homogeneous ...
The energy function in the action principles is not the total energy (conserved in an isolated system), but the Lagrangian, the difference between kinetic and potential energy. The kinetic energy combines the energy of motion for all the objects in the system; the potential energy depends upon the instantaneous position of the objects and ...
Similarly, the kinetic energy of the pendulum mass is defined by the velocity of the pendulum around the pivot to yield = = =. This shows that the quantity I = m r 2 {\displaystyle I=mr^{2}} is how mass combines with the shape of a body to define rotational inertia.
By conservation of energy, assuming the datum is defined at the equilibrium position, when the spring reaches its maximal potential energy, the kinetic energy of the mass is zero. When the spring is released, it tries to return to equilibrium, and all its potential energy converts to kinetic energy of the mass.