# Car suspensions problem

1. Jan 11, 2008

### Oerg

1. The problem statement, all variables and given/known data
Ok, I was stumped by this simple online quiz which asked the variation of acceleration with time of a suspension unit of a car after a road bump which follows SHM. (HC0809)

A. Straight line
B. Ellipse
C. Circle
D. Parabola

3. The attempt at a solution

The answer was supposed to be sinusoidal and the quiz gave the answer as A, straight line but that is obviously wrong since

$$a=-w^2x$$

And the correct form is

$$a=-w^2x_0sinwt$$

Am i missing something, is the quiz wrong

Last edited: Jan 11, 2008
2. Jan 11, 2008

### mda

Was that the exact wording? Maybe there is something you've missed...

Real suspensions also have damping and under particular conditions the oscillation is barely observable... but I don't think a "straight line" would ever be correct for the acceleration.

3. Jan 11, 2008

### Kushal

nooooooo....... the acceleration-displacement graph is a negative gradient straight line, through origin. and the equation is a = -w^2X0

at least this is what we learn in high school.....

4. Jan 11, 2008

### blochwave

If you graph acceleration vs. displacement it is indeed a straight line

with a slope of -w^2, as given by his equation a=-w^2*x

However that's not what he was asked for, unless he read the question wrong. Maybe the question made that slip up

5. Jan 11, 2008

### Oerg

yes there was damping mentioned in the question but I dont see how a straight line could every beformed if the graph was an acceleration time one