# Application Area 9: Appliance Design

A mechanical accelerometer is used to measure the acceleration of a rocket test sled. It contains a linear spring-damper system. See the image below. By tuning the stiffness and damping, the accelerometer can be designed to estimate the acceleration it feels within an acceptable time.

Objective
We can compute the deviation of any system response $x$ from its target value ${x}^{*}$ as follows:
(1)
(2)
The problem is formulated as:
Design Variables
The stiffness of the spring, $k$ , and its damping, $c$ , are the design variables.
Results
By properly selecting the spring stiffness and damping, the accelerometer can be designed to respond in the desired time frame.