What causes the acceleration of a car's suspension after hitting a road bump?

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The discussion centers on a quiz question regarding the acceleration of a car's suspension after hitting a road bump, which is expected to follow simple harmonic motion (SHM). The quiz incorrectly states that the variation of acceleration with time is a straight line, while the correct representation should be sinusoidal, as indicated by the equation a = -w²x₀sin(wt). Participants highlight that while the acceleration-displacement graph is a straight line with a negative gradient, the acceleration-time graph should not be linear due to the oscillatory nature of SHM. Damping effects in real suspensions complicate the motion, but the fundamental principles of SHM suggest that a straight line cannot accurately depict acceleration over time. The consensus is that the quiz question may have been misworded or misunderstood.
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Homework Statement


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

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
 
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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.
 
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...
 
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
 
mda said:
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.

yes there was damping mentioned in the question but I don't see how a straight line could every beformed if the graph was an acceleration time one
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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