0
$\begingroup$

Imagine a damped driven mass spring system with a time-dependent damping coefficient
\begin{equation} m\frac{d^2x}{dt^2} + b(t)\frac{dx}{dt} + kx = F_0 cos(wt) \end{equation} \begin{equation} b(t) = \begin{cases} b_1 & t< t_0\\ b_2 & t\geq t_0 \end{cases} \end{equation}

I am trying to understand how the system would respond to the change in damping coefficient at $t = t_0$. Can we talk about a transient response in that case?

The concept of transient response is often explained with respect to initial conditions of a system and its input signal. I never saw an example where the system's response to a change in internal parameter is investigated.

$\endgroup$

1 Answer 1

0
$\begingroup$

Can we talk about a transient response in that case?
Yes, as in effect you are considering a new system with initial conditions set at $t=t_0$.

Just think about what would happen if you set $b_2=0$.
Then you would expect the system to undergo undamped simple harmonic motion with the initial conditions set at $t=t_0$.

$\endgroup$
1
  • $\begingroup$ I see. Then, the transient response will be determined by the new system's parameters. $\endgroup$
    – Krlngc
    Dec 22, 2021 at 14:05

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.