# Mass-spring system (not exactly homework)

• negation
In summary, a mass-spring system is a physical system consisting of a mass attached to a spring that can oscillate back and forth due to the restoring force of the spring. The equation of motion for this system is F = -kx, where F is the force exerted by the spring, k is the spring constant, and x is the displacement of the mass. The frequency of the system is affected by the mass, spring constant, and amplitude of oscillations, with a higher frequency for a lighter mass, higher spring constant, and larger amplitude. Energy is conserved between potential and kinetic energy in a mass-spring system, with no energy being lost. Real-life applications of mass-spring systems include musical instruments, car suspension
negation
Case of a spring with a mass,m, that has been stretch beyond the equilibrium in the positive x direction.

mg + (-kx0) = 0
k = mg/x0

stretch:

F = mg+ [-k(x0+x1)] = mg-kx0-kx1
but since mg-kx0 = 0
F = 0-kx1 = ma

ma = -kx1
a = -kx1/m

How do I arrive at the corollary from a = - kx1/m to ω0 = SQRT[k/x]?

##a = -kx_1## can be expressed as ##d^2x / dt^2 = -kx_1##

Now it comes down to fitting a solution to this differential equation...

## What is a mass-spring system?

A mass-spring system is a physical system that consists of a mass (or multiple masses) attached to a spring. The mass is free to oscillate back and forth due to the restoring force of the spring.

## What is the equation of motion for a mass-spring system?

The equation of motion for a mass-spring system is given by F = -kx, where F is the force exerted by the spring, k is the spring constant, and x is the displacement of the mass from its equilibrium position.

## What factors affect the frequency of a mass-spring system?

The frequency of a mass-spring system is affected by the mass of the object attached to the spring, the spring constant, and the amplitude of the oscillations. The frequency is higher for a lighter mass, higher spring constant, and larger amplitude.

## How is energy conserved in a mass-spring system?

In a mass-spring system, energy is conserved between potential energy (stored in the spring when it is stretched or compressed) and kinetic energy (when the mass is in motion). As the mass oscillates, the energy is transferred back and forth between these two forms, with no energy being lost.

## What are some real-life applications of mass-spring systems?

Mass-spring systems have many real-life applications, including in musical instruments (such as guitar strings), car suspension systems, and earthquake-resistant buildings. They are also used in scientific experiments, such as in Hooke's law experiments.

• Introductory Physics Homework Help
Replies
8
Views
491
• Introductory Physics Homework Help
Replies
2
Views
203
• Introductory Physics Homework Help
Replies
3
Views
486
• Introductory Physics Homework Help
Replies
3
Views
951
• Introductory Physics Homework Help
Replies
24
Views
1K
• Introductory Physics Homework Help
Replies
14
Views
2K
• Introductory Physics Homework Help
Replies
5
Views
2K
• Introductory Physics Homework Help
Replies
2
Views
282
• Introductory Physics Homework Help
Replies
2
Views
1K
• Introductory Physics Homework Help
Replies
40
Views
2K