Differential equations: spring oscillation

In summary, the conversation discusses finding the value of y (as in yu'(t)) in a spring system with a force of 3 N and a mass of 2kg. The system also includes a damper exerting 3 N when the velocity is 5m/sec. The use of energy equations is suggested as a possible method for finding y. However, the presence of a dampening effect may affect the accuracy of this method. A visual representation of the system may provide further insight.
  • #1
seang
184
0
A spring is stretched 10cm by a force of 3 N. A Mass of 2kg is hung from the spring and attached to a damper which exerts 3 N when the velocity = 5m/sec. There's more but I just need a little help setting it up. I don't understand how to find y (as in yu'(t)). Unless its just 3/5.

Just a few hints would suffice, I'm not asking you to solve these.

Thanks, Sean
Also, I'm sorry I also posted this in the physics homework area. oopsies.
 
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  • #2
have you tried using energy equations like:

m*g*height = (m*v^2)/2
 
  • #3
greytomato said:
have you tried using energy equations like:

m*g*height = (m*v^2)/2

I don't think that'll work since energy is not conserved (there is a dampening affect present).
 
  • #4
uh then i don't understand your question properly... is there a drawing of it?
 

FAQ: Differential equations: spring oscillation

What is a differential equation?

A differential equation is a mathematical equation that describes the relationship between a function and its derivatives. It involves one or more derivatives of an unknown function and is often used to model real-world phenomena.

How are differential equations used to model spring oscillation?

Differential equations are used to model spring oscillation by describing the motion of the spring as a function of time. This is typically done by using Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position.

What is the difference between a simple and damped spring oscillation?

A simple spring oscillation is one in which there is no external force or friction acting on the spring, causing it to oscillate indefinitely. In contrast, a damped spring oscillation is one in which there is some form of external force or friction that causes the oscillations to gradually decrease in amplitude over time.

How do we solve differential equations for spring oscillation?

To solve differential equations for spring oscillation, we can use methods such as separation of variables, variation of parameters, or Laplace transforms. These methods involve manipulating the equations to isolate the dependent variable and then solving for its value at different points in time.

What are some real-life applications of differential equations in spring oscillation?

Differential equations are used in many real-life applications of spring oscillation, including modeling the motion of a car suspension, designing shock absorbers for vehicles, analyzing the movement of a pendulum, and studying the behavior of a vibrating guitar string.

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