@article{MAKHILLJEAS201914617585,
    title = {Influence of Homogenous Part on the Total Solution to the Differential
Equation of SDOF System Response under Harmonic Loading},
    journal = {Journal of Engineering and Applied Sciences},
    volume = {14},
    number = {6},
    pages = {1853-1859},
    year = {2019},
    issn = {1816-949x},
    doi = {jeasci.2019.1853.1859},
    url = {https://makhillpublications.co/view-article.php?issn=1816-949x&doi=jeasci.2019.1853.1859},
    author = {Israa},
    keywords = {Homogenous solution,particular solution,steady state response,damping ratio,SDOF,harmonic
loading},
    abstract = {The problem of SDOF response under harmonic load is usually faced the engineers in their design
life. SDOF represents many structures in practice such as elevated liquid tower or tank. Any equipments or
machines inside structure can exert a harmonic loading on the structure itself. The objective of this research
is to find the complete solution to the differential equation of SDOF structure under sinusoidal loading. Further,
state when the designer or mathematician can neglect the homogonous part of the total solution and when this
part has a significant effect on the total solution. In this study, mathematics of the differential equation for
particular solution is extended to include the homogenous solution. MATLAB was used to plot the
homogenous, particular and the total solutions for the covering differential equation. Many solution variables
(excitation frequency, loading frequency ratio and viscous damping ratio) were used to test the results obtained
and generalized the solution. From the data collected, it was concluded when the homogenous solution part
was neglected from the total solution, the results will have an error which depends on the value of the damping
ratio and the time at which the total solution evaluated. If the value of the damping ratio is small, large window
of time required to minimums the error. While a small windows of time required when the damping ratio has a
larger values.}
    }