Solving the Oscillation of Mass-Spring System

In summary, the conversation is about a problem involving a mass attached to a spring with a resistive force and constants A, B, and k. The conversation includes discussing the differential equation and solving for the solution. The question of finding the fractional change in amplitude of oscillation is also brought up and eventually resolved.
  • #1
bon
559
0

Homework Statement



Mass m attached to spring with spring constant k=Am. It feels a resistive force magnitude Bmv where v is the speed. and A, B are constants such that 4A > B^2

What is the fractional change in amplitude of oscillation in one complete oscillation?


Homework Equations





The Attempt at a Solution



Ok so I've written down the DE:

x'' + Bx' - Ax = 0 and solved..but this gives be Ce^-Lt + De^-L't where C, D, L and L' are constants...

1) i don't see how this oscillates... 2) how do i work out fractional change in amplitude of oscillation?
 
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  • #2
Hi bon! :smile:

(try using the X2 tag just above the Reply box :wink:)
bon said:
Mass m attached to spring with spring constant k=Am. It feels a resistive force magnitude Bmv where v is the speed. and A, B are constants such that 4A > B^2
…
x'' + Bx' - Ax = 0

Nooo :redface:
 
  • #3
Why not? I thought this was a direct consequence on NII (and cancelling the m)
 
  • #4
One of the signs is wrong. :wink:
 
  • #5
ok i see thanks i can now solve the eqn but how do i find fractional change in amplitude of oscillation
 
  • #6
Well, what's your solution now? :smile:
 
  • #7
not to worry - i get it now. thanks
 

Related to Solving the Oscillation of Mass-Spring System

1. What is a mass-spring system?

A mass-spring system is a physical system that consists of a mass attached to a spring. The mass is free to move along a straight line, while the spring is either compressed or stretched. The system exhibits oscillatory motion when disturbed from its equilibrium position.

2. What causes the oscillation in a mass-spring system?

The oscillation in a mass-spring system is caused by the interplay between the restoring force of the spring and the inertia of the mass. When the mass is displaced from its equilibrium position, the spring exerts a force that tries to bring it back to the equilibrium point. However, the mass's inertia causes it to overshoot the equilibrium position, resulting in a back-and-forth motion.

3. How can the oscillation of a mass-spring system be solved?

The oscillation of a mass-spring system can be solved using the equation of motion, which is derived from Newton's second law of motion. This equation takes into account the mass, spring constant, and displacement of the mass from its equilibrium position. By solving this equation, we can determine the amplitude, frequency, and period of the oscillation.

4. What factors affect the oscillation of a mass-spring system?

The key factors that affect the oscillation of a mass-spring system are the mass, spring constant, and initial displacement. A higher mass or stiffer spring will result in a slower oscillation with a longer period. On the other hand, a lower mass or less stiff spring will cause a faster oscillation with a shorter period. The initial displacement determines the amplitude of the oscillation.

5. How is the oscillation of a mass-spring system useful in real-life applications?

The oscillation of a mass-spring system has many real-life applications, such as in the suspension system of vehicles, musical instruments, and shock absorbers. It is also used in timekeeping devices like pendulum clocks and mechanical watches. Understanding and solving the oscillation of mass-spring systems is crucial in designing and optimizing these systems for various applications.

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