Question

When a car drives over a speed bump and oscillates up and down in simple harmonic motion, at which position during the motion is the acceleration of the car the greatest?

Answer 1

At its uppest and lowest position

Step-by-step explanation:

In a simple harmonic motion, the acceleration is given by:

`a(t)=-\omega^2 x(t)`

where

`\omega` is the angular frequency of the motion

x(t) is the displacement of the object from the equilibrium position

So we see that the acceleration is directly proportional to the displacement. Therefore, in this situation, the acceleration of the car will be greatest when the displacement is also greatest: so, when the car is at its uppest position and when it is at its lowest position.