What is undamped free vibration?
The simplest vibrations to analyze are undamped, free, one degree of freedom vibrations. "Undamped" means that there are no energy losses with movement (whether intentional, by adding dampers, or unintentional, through drag or friction). An undamped system will vibrate forever without any additional applied forces.
How to Calculate Particular Integral?
Particular Integral calculator uses Particular Integral = (Static Force*cos(Angular Velocity*Time Period-Phase Constant))/(sqrt((Damping Coefficient*Angular Velocity)^2-(Stiffness of Spring-Mass suspended from Spring*Angular Velocity^2)^2)) to calculate the Particular Integral, The Particular integral formula is defined as a part of solution of the differential equation of forced undamped vibrations. Particular Integral is denoted by x2 symbol.
How to calculate Particular Integral using this online calculator? To use this online calculator for Particular Integral, enter Static Force (Fx), Angular Velocity (ω), Time Period (tp), Phase Constant (ϕ), Damping Coefficient (c), Stiffness of Spring (k) & Mass suspended from Spring (m) and hit the calculate button. Here is how the Particular Integral calculation can be explained with given input values -> 121701.4 = (20*cos(10*1.2-0.785398163397301))/(sqrt((5*10)^2-(60-0.25*10^2)^2)).