Vibration it can be very harmful – leading to eventual failure of the system. Consequently, one of the major reasons for vibration analysis is to predict when this type of resonance may occur and then to determine what steps to take to prevent it from occurring. As the amplitude plot shows, adding damping can significantly reduce the magnitude of the vibration. Also, the magnitude can be reduced if the natural frequency can be shifted away from the forcing frequency by changing the stiffness or mass of the system. If the system cannot be changed, perhaps the forcing frequency can be shifted
Kinetic theory of gases can calculate the number of atomic or molecular collisions with a wall of a container per unit area per unit time. Assuming an ideal gas, a derivation results in an equation for total number of collisions per unit time per area: This quantity is also known as the "impingement rate" in vacuum physics. From the kinetic energy formula it can be shown that where "v" is in m/s, "T" is in kelvins, and "m" is the mass of one molecule of gas. The most probable (or mode) speed formula_26 is 81.6% of the rms speed formula_27, and the mean (arithmetic