Oscillation of a vertical spring

Click For Summary
The discussion revolves around the oscillation of a mass attached to a vertical spring, focusing on deriving the frequency of small oscillations and the governing equations when the spring's top end is oscillated. The frequency for small oscillations is derived as ω = √(g/(b-a)), using the equilibrium condition and the formula for the period of a mass-spring system. For the second part, participants analyze the effects of an external driving force on the spring's length, leading to the equation of motion that includes terms for both the spring's extension and the external oscillation. The conversation emphasizes the importance of correctly identifying forces and sign conventions in the equations. The overall analysis highlights the complexities of dynamic systems involving oscillations and the need for careful mathematical treatment.
  • #61
See the figure: It shows the time dependence of both the length L and the position of the mass, (y) for the case when w=2pi, n=4pi, c=0.1 b=1.Note how much less the mass moves compared to the spring.

Also watch the video about an experiment with a slinky. The top of the slinky is released and falls down, while the mass at the bottom stays almost motionless except the last stage when the slinky gets relaxed.

http://www.youtube.com/watch?v=oKb2tCtpvNU&NR=1

ehild
 

Attachments

  • springy.jpg
    springy.jpg
    22.7 KB · Views: 440

Similar threads

Two spring-coupled masses in an electric field (one of the masses is charged)
  • · Replies 1 ·
Replies
1
Views
1K
Estimating damped harmonic oscillator parameters from this plot of the oscillations
  • · Replies 9 ·
Replies
9
Views
2K
Inclined plane with pulley and spring
  • · Replies 10 ·
Replies
10
Views
3K
Initial velocity of bird landing on horizontal wire modeled as spring
  • · Replies 7 ·
Replies
7
Views
1K
Calculate the spring constant of oscillating mass on a spring colliding with a wall
  • · Replies 31 ·
2
Replies
31
Views
2K
Difference between resonance in undamped vs damped mass-spring-dashpot
  • · Replies 17 ·
Replies
17
Views
3K
Two bodies connected with an elastic thread moving with friction
  • · Replies 6 ·
Replies
6
Views
1K
Max amplitude of a diving board that will not toss a pebble off?
  • · Replies 39 ·
2
Replies
39
Views
3K
Force transmitted to a block in viscous fluid through a spring, cord, and pulley
  • · Replies 6 ·
Replies
6
Views
954
How to solve a differential equation for a mass-spring oscillator?
  • · Replies 2 ·
Replies
2
Views
2K