Design and Analysis of an oil Cushion

1973 ◽  
Vol 15 (1) ◽  
pp. 48-52 ◽  
Author(s):  
M. A. Satter
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Linear Equation ◽  
Dynamic Characteristics ◽  
Order Linear Differential Equation ◽  
First Order ◽  
Non Linear Equation ◽  
Non Linear ◽  
Linear Differential ◽  
Good Agreement

The dynamic characteristics of an oil cushion, which was originally designed to eliminate impactive excitation to a mechanical lever and thereby achieve noise reduction, have been studied both theoretically and experimentally. The system motion is represented by a second order non-linear differential equation which can be reduced to a first order linear differential equation by changing the variables. An approximate but simple solution to the non-linear equation has also been presented. Theoretical and experimental results have good agreement.

4. On the Linear Differential Equation of the Second Order

1878 ◽  
Vol 9 ◽  
pp. 93-98 ◽  
Author(s):  
Tait
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Linear Equation ◽  
Arbitrary Constant ◽  
Second Order ◽  
General Linear ◽  
First Order ◽  
Non Linear Equation ◽  
Non Linear ◽  
Linear Differential

This paper contains the substance of investigations made for the most part many years ago, but recalled to me during last summer by a question started by Sir W. Thomson, connected with Laplace's theory of the tides.A comparison is instituted between the results of various processes employed to reduce the general linear differential equation of the second order to a non-linear equation of the first order. The relation between these equations seems to be most easily shown by the following obvious process, which I lit upon while seeking to integrate the reduced equation by finding how the arbitrary constant ought to be involved in its integral.

scholarly journals Oscillation of first order linear differential equations with several non-monotone delays

2018 ◽  
Vol 16 (1) ◽  
pp. 83-94
Author(s):  
E.R. Attia ◽  
V. Benekas ◽  
H.A. El-Morshedy ◽  
I.P. Stavroulakis
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Linear Differential Equation ◽  
Linear Differential Equations ◽  
Order Linear Differential Equation ◽  
Order Linear ◽  
First Order ◽  
Linear Differential

AbstractConsider the first-order linear differential equation with several retarded arguments$$\begin{array}{} \displaystyle x^{\prime }(t)+\sum\limits_{k=1}^{n}p_{k}(t)x(\tau _{k}(t))=0,\;\;\;t\geq t_{0}, \end{array} $$where the functions pk, τk ∈ C([t0, ∞), ℝ+), τk(t) < t for t ≥ t0 and limt→∞τk(t) = ∞, for every k = 1, 2, …, n. Oscillation conditions which essentially improve known results in the literature are established. An example illustrating the results is given.

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