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Hello Sean,
In Figure 3, which shows the plot of absolute support and mass motion, I notice that at t=0, the support motion is zero, yet the absolute steady-state response is not zero. While I understand the phase shift you mentioned in your proof, I’m struggling to grasp conceptually how it’s possible to have a response at t=0 without any support displacement.
Thanks!
Hey @Shakib.Ayoubzadeh - good question.
Here we’re only visualising the steady-state response and have neglected the transient response that would have brought the mass to this state. If we plotted the full transient and steady-state response for the mass, we would see that it does start with zero position and velocity (assuming we imposed these initial conditions) and undergoes a transient oscillation before settling into a steady state-harmonic oscillation (that we see in the plot).
To elaborate a little further…at t=0 in this plot, you’re seeing a snapshot of each mass - the support mass has a position of zero, but it’s velocity is actually at a maximum while the other mass has a maximum position amplitude but at this instant, has zero velocity (as it changes direction).
S