# Optimizing Damping Time: Which Application Would Benefit Most?

• RedEyes
In summary, the question is asking which application would benefit the most from a short damping time. The options are a bathroom scale, child jolly jumper, suspension on a passenger car, and suspension on a race car. It is suggested that both the bathroom scale and race car suspension would benefit from being overdamped, but the question is asking which one would benefit the most.
RedEyes

## Homework Statement

"Which of the following applications would have the most benefit from a short damping time?"
a. bathroom scale
b. child jolly jumper
c. suspension on passenger car
d. suspension on race car

## The Attempt at a Solution

Im assuming that both A and D should be as damped as possible, so its more of a question as to which one has a shorter damping time and/or which one objectively benefits the most from it. Thanks.

I would ask myself: which one, if any, would benefit from being overdamped.

DrClaude said:
I would ask myself: which one, if any, would benefit from being overdamped.
It would be my understanding that both A and D would benefit from being over damped. It is my teacher's opinion (justified or not); however, that one is a better answer. I am trying to figure out which one that is.

## What is damped harmonic motion?

Damped harmonic motion is a type of oscillatory motion where the amplitude of the oscillations decreases over time due to the presence of a damping force. It is commonly observed in systems where energy is dissipated, such as a mass-spring system with a frictional force.

## What factors affect the damping of a system?

The damping of a system is affected by several factors, including the magnitude of the damping force, the physical properties of the system (such as mass and stiffness), and the initial conditions (such as the amplitude and velocity of the oscillations).

## How is damped harmonic motion represented mathematically?

In a system with a damping force proportional to the velocity, damped harmonic motion can be described by the following differential equation: m(d^2x/dt^2) + c(dx/dt) + kx = 0, where m is the mass, c is the damping coefficient, k is the spring constant, x is the displacement, and t is time.

## What is the relationship between damping and frequency in damped harmonic motion?

The frequency of damped harmonic motion is affected by the damping force, with higher damping resulting in a lower frequency. As the damping force increases, the system takes longer to complete each oscillation, resulting in a lower frequency.

## How does the amplitude of damped harmonic motion change over time?

As the system experiences damping, the amplitude of the oscillations decreases over time. The rate at which the amplitude decreases depends on the magnitude of the damping force and the frequency of the oscillations.

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