Harmonic Oscillator With and Without Friction (mass on a spring)

Thread starter quark12
Start date Nov 22, 2020
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Friction Harmonic Harmonic oscillator Oscillator Spring

In summary, the conversation discusses finding the equation of motion and its solution for a mass connected to a spring with coefficient k on a horizontal surface. The mass is initially displaced a distance x0 to the right and released at t=0. The relevant equation is F=-kx. Two cases are considered: a) no friction and b) friction given by F=-b-v, where b is the friction coefficient and v is the velocity of the mass. The differential equations and solutions are required to be written in terms of k, x0, and m only.

Nov 22, 2020

quark12

Homework Statement: A mass m connected to a spring with coefficient k, which is connected to a wall in its other side.The mass is on a horizontal surface and has been displaced a distancex0to the right from equilibrium.At t= 0the mass was released.Find the equation of motion (differential equation) and its solution (in terms of k,x0, and m only) for the following cases:a. No friction.b. The friction between the mass and the surface is given by−→F=−b−→v, where b is the friction coefficient and−→v is the velocity of the mass.

Relevant Equations: F=-kx

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Nov 22, 2020

berkeman

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quark12 said:

Homework Statement:: A mass m connected to a spring with coefficient k, which is connected to a wall in its other side.The mass is on a horizontal surface and has been displaced a distancex0to the right from equilibrium.At t= 0the mass was released.Find the equation of motion (differential equation) and its solution (in terms of k,x0, and m only) for the following cases:a. No friction.b. The friction between the mass and the surface is given by−→F=−b−→v, where b is the friction coefficient and−→v is the velocity of the mass.
Relevant Equations:: F=-kx

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Related to Harmonic Oscillator With and Without Friction (mass on a spring)

1. What is a harmonic oscillator?

A harmonic oscillator is a system that exhibits periodic motion, where the restoring force is directly proportional to the displacement from equilibrium. This type of motion can be seen in various physical systems, such as a mass on a spring or a pendulum.

2. How does a harmonic oscillator with friction differ from one without friction?

A harmonic oscillator with friction experiences a damping force, which decreases the amplitude of the oscillations over time. This means that the oscillations will eventually come to a stop. In contrast, a harmonic oscillator without friction will continue to oscillate indefinitely with the same amplitude.

3. What is the equation of motion for a harmonic oscillator with and without friction?

The equation of motion for a harmonic oscillator without friction is given by m∈ + kx = 0, where m is the mass, k is the spring constant, and x is the displacement from equilibrium. For a harmonic oscillator with friction, the equation of motion becomes m∈ + kx + bv = 0, where b is the damping coefficient and v is the velocity.

4. How does the presence of friction affect the period of oscillation in a harmonic oscillator?

The presence of friction in a harmonic oscillator will decrease the period of oscillation. This is because the damping force acts to decrease the amplitude of the oscillations, causing the system to return to equilibrium faster.

5. Can a harmonic oscillator with friction ever reach equilibrium?

No, a harmonic oscillator with friction will never reach equilibrium. As the oscillations decrease in amplitude, the damping force will also decrease, resulting in smaller and smaller oscillations. However, the oscillations will never completely stop unless an external force is applied to bring the system to equilibrium.