Consider a metal bar of initial length l and cross-sectional area a. the young's modulus of the material of the bar is y. find the "spring constant" k of such a bar for low values of tensile strain.

Spring constant = YA / L

Explanation:

Let F be the force being applied on cross sectional area A of metal bar due to which an extension of ΔL is obtained in the wire of length L then

stress = F / A

strain = ΔL /L

Young's modulus = ( F / A ) / (ΔL /L)

Y = ( F L / A ΔL )

( F / ΔL ) = ( YA / L )

Spring constant = ( F / ΔL )

Spring constant = YA / L

the motion of a pendulum is a classic example of mechanical energy conservation. a pendulum consists of a mass (known as a bob ) attached by a string to a pivot point. as the pendulum moves it sweeps out a circular arc, moving back and forth in a periodic fashion.

this could be newton#'s law of cooling. the cooling curve is exponential