# PhysicsLongitudinal excitation of a sine wave

#### Nino

##### New member
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
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:
$$x = v_x + A_x e^{\displaystyle j\omega_x t}$$