Damping. Altitude vs. Period which has greater effect?

[aaj92]

Homework Statement

This is only part of the problem but this is all I'm having trouble with...

Which effect of damping would be more noticeable, the change of period or the decrease of the amplitude?

Homework Equations

x(t)= Ae$^{-\beta t}$ * cos(w$_{1}$t - $\delta$)

period = $\frac{2Pi}{w_{1}}$

The Attempt at a Solution

so I can sort of make an argument for both but I think I'm leaning more toward the period purely on the fact that w is inside the argument of the cosine so it's effect is smaller than a change in amplitude would be. Is that right? And if it is is it the right logic? because I'm sort of just guessing at this point but it seems to make sense to me...

 

[anathema]

I would like to clarify that the effect of damping on the period and amplitude depends on the specific system and its parameters. In general, damping causes both the period and amplitude to decrease, but the extent to which each is affected depends on the damping coefficient and the natural frequency of the system.

In some cases, the decrease in amplitude may be more noticeable because it directly affects the magnitude of the oscillation. On the other hand, in some systems, the change in period may be more noticeable because it directly affects the frequency of the oscillation.

Therefore, it is important to consider both factors and analyze the specific system in question to determine which effect of damping would be more noticeable. Additionally, it is important to note that both the period and amplitude are equally important in describing the behavior of an oscillating system.