# Differential equation/ spring application

• Punchlinegirl
In summary, the conversation is about determining the value of the coefficient γ for a critically damped system consisting of a mass, spring, and damper. The mass weighs 8 lb and stretches the spring 1.5 in. To solve this, one must review the general solution to the differential equation for damped simple harmonic motion and use the given information to find the spring constant. The standard differential equation for a spring with damper should also be considered.
Punchlinegirl
A mass weighing 8 lb stretches a spring 1.5 in. The mass is also attached to a damper with coefficient γ . Determine the value of γ for which the system is critically damped; be sure to give units for γ .

I have no idea where to start. Can someone help me out?

Punchlinegirl said:
A mass weighing 8 lb stretches a spring 1.5 in. The mass is also attached to a damper with coefficient γ . Determine the value of γ for which the system is critically damped; be sure to give units for γ .

I have no idea where to start. Can someone help me out?
You have to review your text on the general solution to the differential equation for damped simple harmonic motion. There is a good explanation http://hyperphysics.phy-astr.gsu.edu/hbase/oscda.html#c1"

AM

Last edited by a moderator:
Punchlinegirl said:
A mass weighing 8 lb stretches a spring 1.5 in. The mass is also attached to a damper with coefficient γ . Determine the value of γ for which the system is critically damped; be sure to give units for γ .

I have no idea where to start. Can someone help me out?
The fact that "A mass weighing 8 lb stretches a spring 1.5 in." tells you the spring constant. What is the standard differential equation for a spring with damper?

## 1. What is a differential equation?

A differential equation is a mathematical equation that relates an unknown function to its derivatives. It is commonly used to model the behavior of physical systems, such as springs, and to make predictions about their future behavior.

## 2. How are differential equations used in spring applications?

In spring applications, differential equations are used to model the motion of a spring by relating the displacement of the spring to the forces acting on it. This allows us to predict the behavior of the spring under different conditions, such as when a weight is attached to it or when it is stretched or compressed.

## 3. What is a spring constant?

A spring constant, also known as the spring stiffness, is a measure of how stiff or flexible a spring is. It is represented by the letter k and is defined as the force required to stretch or compress a spring by one unit of length.

## 4. How can we solve differential equations for spring applications?

There are several methods for solving differential equations for spring applications, such as using separation of variables, using the method of undetermined coefficients, or using Laplace transforms. These methods involve manipulating the equation to isolate the unknown function and then using mathematical techniques to solve for it.

## 5. What are some real-life applications of differential equations in springs?

Differential equations are used in various real-life applications involving springs, such as in car suspensions, shock absorbers, and bungee jumping. They are also used in engineering design to determine the optimal spring stiffness for different purposes, such as in mattresses or door hinges.

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