# Help finding equation of motion

• bengaltiger14
In summary, the conversation discusses a problem involving a 1/4kg mass attached to a spring with a stiffness of 4N/m and a damping constant of 1 N-sec/m. The equation of motion for this system is (m)y(doubleprime(t)) + gamma(y prime(t)) + ky(t)=0, where m = 0.25kg/(9.81 m/second^2), gamma = 1N-s/m, and k = 4N/m. The maximum displacement of the mass can be found by solving for y(t) using the given boundary conditions.

## Homework Statement

A 1/4kg mass is attached to spring with stiffness of 4N/m. The damping constant for the system is 1 N-sec/m. If the mass is displaced 1/2 meter up and given an initial velocity of 1 m/sec upward, find the equation of motion. What is the maximum displacement that the mass will attain??

I don't know how to get started with this. I know the spring equation Fs=-kx. So, Fs would just equal 1 N Kg/m. I just don't know what to do. Any help would be appreciated.

Since you posted this in Introductory Physics I assume you aren't familiar with differential equations. In that case you would have to have been taught the equation of motion for a damped oscillator. Is that the case? Are there any equations that your teacher has presented on this?

I have the equation: (m)y(doubleprime(t)) + gamma(y prime(t)) + ky(t)=0

m = .25kg/(9.81 m/second^2)
gamma = 1N-s/m k=4N/m

so, the equation of motion is:

0.025y(doubleprime) + y(prime) + 4y=0

And for an equation of that type, do you know how to solve for y(t)? If you have the general technique, you should be able to enter in your boundary conditions (initial speed, initial displacement) during intermediate steps to get to an expression for displacement.

## What is an equation of motion?

An equation of motion is a mathematical representation of the motion of an object, describing its position, velocity, and acceleration at any given time. It helps to predict the future motion of an object based on its initial conditions and external forces acting on it.

## What are the types of equations of motion?

There are three main types of equations of motion: linear, rotational, and projectile. Linear equations of motion describe the motion of an object in a straight line, while rotational equations of motion describe the motion of an object around an axis. Projectile equations of motion are used to describe the motion of an object in a projectile path, such as a ball being thrown.

## How do I find the equation of motion for a given scenario?

To find the equation of motion for a given scenario, you will need to gather information about the initial conditions and external forces acting on the object. This includes the object's initial position, velocity, and acceleration, as well as any forces acting on it such as gravity or friction. Then, you can use the appropriate equation of motion (linear, rotational, or projectile) to solve for the object's motion over time.

## What are the key variables in an equation of motion?

The key variables in an equation of motion are position (x), velocity (v), acceleration (a), time (t), and initial conditions (x0, v0, a0). These variables are used to describe the motion of an object and can be solved for using the appropriate equation of motion.

## Why is it important to understand equations of motion?

Equations of motion are important because they allow us to predict the future motion of an object and understand how external forces affect that motion. They are essential in fields such as physics, engineering, and astronomy, and are used to solve real-world problems and make accurate predictions about the behavior of objects in motion.