The foundation of a reciprocating engine is subjected to harmonic motions in \(x\) and \(y\) directions:

\[\begin{aligned}& x(t)=X \cos \omega t \\& y(t)=Y \cos (\omega t+\phi)\end{aligned}\]

where \(X\) and \(Y\) are the amplitudes, \(\omega\) is the angular velocity, and \(\phi\) is the phase difference.

a. Verify that the resultant of the two motions satisfies the equation of the ellipse given by (see Fig. 1.111):

b. Discuss the nature of the resultant motion given by Eq. (E.1) for the special cases of \(\phi=0, \phi=\frac{\pi}{2}\), and \(\phi=\pi\).

Transcribed Image Text:

y2 xy 2 cos = sin XY (E.1)