# Simple Harmonic Motion and a Car

• stanli121
In summary, the conversation discusses how a car accelerates uniformly and how an open door that slams shut will do so in simple harmonic motion. Various equations and ideas are explored, such as using torque and force to calculate the motion of the door. The suggestion is made to consider other axes for calculating torque in order to solve the problem.
stanli121

## Homework Statement

A car uniformly accelerates. Show an open door that slams shut will do so in simple harmonic motion.

## The Attempt at a Solution

This seems more conceptual than mathematical. I considered using T = Ia but the problem is the torque would act on the pivot (point where door connects to car) and be R=0 from the axis so T=0. Then I considered F=ma because the acceleration is known to be constant. But I ran into two problems there. First, the displacement I would need to relate to acceleration to show SHM is not clear whatsoever. Second, wouldn't the force about the pivot be centripetal, thus removing my x and d2x/dt2? My newest thought is perhaps choosing a point on the pavement and doing some sort of T = dL/dt type calculation then relating $$\theta$$ and $$\alpha$$ that way. Any comments on my ideas or new ideas?
Thanks.

Last edited:
You can calculate the torque around any axis. You're probably used to using pivot points because that's usually the convenient thing to do, but in this case you might want to consider other axes to try.

You are correct in thinking that this problem is more conceptual than mathematical. To show simple harmonic motion in this scenario, we can consider the door as a pendulum. When the car accelerates, the door will swing open due to the inertia of the door. As the car continues to accelerate, the door will reach its maximum displacement and start to swing back towards the closed position. This back-and-forth motion of the door can be described as simple harmonic motion, with the car's acceleration acting as the restoring force.

To relate this to the equations of simple harmonic motion, we can consider the door's displacement from the closed position as the x-coordinate in our equation x = A*sin(ωt), where A is the amplitude and ω is the angular frequency. As the car continues to accelerate, the door's displacement will change sinusoidally, creating a smooth, back-and-forth motion.

In summary, the car's acceleration acts as the restoring force for the door, causing it to exhibit simple harmonic motion. This example highlights the wide applicability of simple harmonic motion in various physical systems.

## 1. What is Simple Harmonic Motion?

Simple Harmonic Motion (SHM) is a type of periodic motion in which an object oscillates back and forth around an equilibrium point with a constant amplitude and a constant period. It is characterized by a sinusoidal or wave-like motion.

## 2. How is Simple Harmonic Motion related to a car?

Simple Harmonic Motion can be observed in a car's suspension system, where the car's body moves up and down in response to bumps on the road. This motion is similar to the motion of a pendulum or a spring.

## 3. What factors affect the frequency of Simple Harmonic Motion in a car?

The frequency of Simple Harmonic Motion in a car is affected by the stiffness of the suspension system, the mass of the car, and the damping force. A stiffer suspension system will have a higher frequency, while a heavier car and a stronger damping force will have a lower frequency.

## 4. How does Simple Harmonic Motion affect a car's ride comfort?

In general, a higher frequency of Simple Harmonic Motion in a car's suspension system can result in a bumpier ride, while a lower frequency can provide a smoother ride. However, the design of the suspension system and the damping force can also play a significant role in ride comfort.

## 5. Can Simple Harmonic Motion be used to improve a car's handling?

Yes, Simple Harmonic Motion is an important factor in a car's handling. By adjusting the frequency of the suspension system, engineers can improve a car's stability and reduce body roll during turns. However, other factors such as tire grip and weight distribution also play a role in a car's handling.

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