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Physics Longitudinal excitation of a sine wave

Nino

New member
Oct 22, 2013
1
Hi!
This is a problem regarding a quarter car model driving over a sinusoidal road excitation.

A sinusoidal excitation can be written on the form ze^(jωt), z being vertical. I would like to write the longitudinal excitation of a sine wave on the same form?

Any hints and tips are much appreciated.
 
Last edited:

Klaas van Aarsen

MHB Seeker
Staff member
Mar 5, 2012
8,774
Hi!
This is a problem regarding a quarter car model driving over a sinusoidal road excitation.

A sinusoidal excitation can be written on the form ze^(jωt), z being vertical. I would like to write the longitudinal excitation of a sine wave on the same form?

Any hints and tips are much appreciated.
Welcome to MHB, Nino! :)

Looks like your z-coordinate is of the form \(\displaystyle z=A_z e^{j\omega_z t}\), where $A_z$ is an amplitude and $\omega_z$ is the angular frequency for the excitation in the z direction.

If that was your intention, you can use a similar formula for your x coordinate.
Assuming your car model drives in the x direction with some average speed $v_x$, a possible formula for the x coordinate is:
$$x = v_x + A_x e^{\displaystyle j\omega_x t}$$