• The mass m has zero velocity when first dropped, And also when the spring is deflected through the maximum dynamic deflection. Equating the resultant work done on mass to the zero change in kinetic energy, we therefore obtain*
Where mg is the work done by gravity on the body, and 1 is the resisting work done by the equivalent spring.
If Eq. 1 is rearranged in the formถ้า Eq. 1
and mg/k is replaced which is the static deformation produced by a gradual application of the weight mg, the following general value of 2 is obtained: Tow extreme cases are of interest. If h is large compared with 2, we may neglect the work mg2 in Eq. (a), which then reduces to
In the other extreme case, h = 0 (i.e., the load is suddenly applied) and Eq. (a) reduces to