91Ó°ÊÓ

A single degree of freedom system is represented as a \(4 \mathrm{~kg}\) mass attached to a spring possessing a stiffness of \(6 \mathrm{~N} / \mathrm{m}\). Determine the response of the horizontally configured system if the mass is displaced 2 meters to the right and released with a velocity of \(4 \mathrm{~m} / \mathrm{sec}\). What is the amplitude, period and phase lag for the motion? Sketch and label the response history of the system.

Determine the natural period of a typical ice cube floating in water. Measure the dimensions of a typical cube from your refrigerator and calculate its natural frequency in water. (The dimensions may vary depending on your particular ice tray.) Confirm your "experiment." Place an ice cube in water, displace it slightly and release it. Make an approximate measure of the period of an oscillation with your wrist watch, or a stop watch if available. Repeat this operation several times and compare the average measured value with the calculated value.

Determine the overshoot of the system of Problem \(2.25\) if it is critically damped and \(v_{0}=-4 \mathrm{~m} / \mathrm{sec}\).