You have a prototype Slinky with a lump of coal at the end. This forms a damped spring-mass system. Assuming the usual units you may suppose the mass of the coal m=1, k=3, and the damping constant b = 1. Write down an ODE that models the behavio of this system. If you stretch the spring 1 meter and let it go with no initial velocity, determine the position of the mass after t seconds.

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Fire safety

Fire safety is a new domain emerged in the early 90s to enable the design of buildings, structures, and infrastructure against destruction through fire. It also includes the provisions of building codes. This field is mostly associated with the design and efficient planning of a building, to reduce the destruction caused by fire. The branch of engineering that deals with it for the safety of the buildings from destruction of fire, is known as fire safety engineering.