Why Critical damping is often the goal of Mechanical engineers in designing systems?Fig: A Damped Oscillation
Why Critical damping is often the goal of Mechanical engineers in designing systems?
Fig: A Damped Oscillation
From figure it can be noted that amplitude decreases exponentially which is the case for a damped oscillation,
A undamped oscillation isn't acted by any opposing force meaning it oscillates indefinitely.
But a damped oscillation is acted by another opposing force of damping constant b which is what we see in our daily life.
where, tau is damping time constant that is the time taken to decrease exponentially by 1/e of its initial value and
Since, the mechanical engineers doesn't want unwanted and harmful oscillations, the required condition is ω'=0 which is the case for critical damping. Also, the motion decays exponentially to zero with no oscillation at all.
For the above case, damping constant should be 2(k m)1/2., it also follows τ=1/ω which is the shortest possible value of damping time constant.
So, Critical damping always roams in the mind of Mechanical engineers.