# Solving the Displacement of Particle on a Stretchy Spring

• vortec135
Instead, you need to find the displacement of the particle from the equilibrium position at a specific time (t=0.5s). To do this, you will need to use the equation of motion and solve for x(t). Once you have x(t), you can plug in t=0.5s to find the displacement at that specific time. In summary, the problem involves a spring with a negligible mass, a 0.500-kg particle, and a horizontal surface with no friction. The spring stretches 3.00 cm from its relaxed length when a force of 7.50 N is applied. The particle is then pulled horizontally, stretching the spring 5.00 cm, and released from rest at t=
vortec135

## Homework Statement

A spring of negligible mass stretches 3.00 cm from its relaxed length when a force of 7.50 N is applied. A 0.500-kg particle rests on a frictionless horizontal surface and is attached to the free end of the spring. The particle is pulled horizontally so that it stretches the spring 5.00 cm and is then released from rest at t=0. Determine the displacement x of the particle from the equilibrium position at t=0.500s.

Not sure

## The Attempt at a Solution

I've calculated the spring constant, the average acceleration from the stretched position to the equilibrium solution but I can't do anything to solve for time..

Can anyone tell me how to solve this question?

Sounds like what you need to do is to write the equation of motion (a differential equation), solve the differential equation, and then evaluate x(t=0.5) after you have found x(t) as the solution of the differential equation.

There is no solving for the time involved in this problem.

## What is the "displacement of a particle on a stretchy spring"?

The displacement of a particle on a stretchy spring refers to the distance the particle moves from its original position when the spring is stretched or compressed. It is a measure of how far the particle has moved along the spring's length.

## What factors affect the displacement of a particle on a stretchy spring?

The displacement of a particle on a stretchy spring is affected by the amount of force applied to the spring, the stiffness of the spring, and the mass of the particle. These factors determine how much the spring will stretch or compress and therefore, how far the particle will move.

## How is the displacement of a particle on a stretchy spring calculated?

The displacement of a particle on a stretchy spring can be calculated using Hooke's Law, which states that the displacement is directly proportional to the force applied and inversely proportional to the stiffness of the spring. The formula for calculating displacement is: x = F/k, where x is the displacement, F is the force, and k is the spring constant.

## Why is it important to solve for the displacement of a particle on a stretchy spring?

Solving for the displacement of a particle on a stretchy spring is important because it allows us to understand the behavior and properties of a spring. It also has practical applications in various fields such as engineering, physics, and materials science.

## What are some real-life examples of the displacement of a particle on a stretchy spring?

One example of the displacement of a particle on a stretchy spring is a car's suspension system, where the springs compress and stretch as the car moves over bumps and dips in the road. Another example is a pogo stick, where the spring compresses and stretches as the user bounces up and down. Additionally, many household items such as mattresses, trampolines, and door hinges rely on the displacement of a particle on a stretchy spring to function properly.

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