Overshoot of 15% what is damping ratio

[Dustinsfl]

Homework Statement

A shock absorber is to be designed to limit its overshoot to $15$ percent of its initial displacement when released. Find the damping ratio $\zeta_0$ required.

Homework Equations

The Attempt at a Solution

My question is since log decrement, $\delta = \ln\frac{x_1}{x_2} = \frac{2\pi\zeta}{\sqrt{1 - \zeta^2}}$, for a 15% overshoot, do I set $\frac{x_1}{x_2} = 1.15$ and then solve for $\zeta$?

 

[mfb]

How is overshoot defined? In the way you use it it looks odd (1000% overshoot would mean a strong damping then).
Also make sure you use the correct amplitudes to compare - after 1/2 of the oscillation or a full oscillation?

 

[donpacino]

My question is since log decrement, $\delta = \ln\frac{x_1}{x_2} = \frac{2\pi\zeta}{\sqrt{1 - \zeta^2}}$, for a 15% overshoot, do I set $\frac{x_1}{x_2} = 1.15$ and then solve for $\zeta$?

yes