# Spring and resonance

1. Nov 19, 2005

### Atomos

I am asked to explain why an oscillation spring will eventually begin oscillating in the horizontal direction, i.e. become a pendulum, and I am asked why a mass that is too great will not become a pendulum.

I know the answer to the first part of the question. The spring has a natural tendency to twist when stretched. This twisting produces a small force in the sideways direction that adds to the amplitude of the side to side oscillation every time the spring is fully stretched. However, I am not sure why this effect is reduced or eliminated with increased mass. Is it because the heavier mass has more inertia and thus does not twist as easily?

2. Nov 19, 2005

### lightgrav

Careful ... twisting of the spring produces torque around a vertical axis,
but this is not really an external horizontal Force. It would result in a
significant "Torsional oscillation" if the torque / rotational inertia has
the same natural frequency of oscillation as the vertical oscillation mode. With care, these modes can be made to alternate (google "wilberforce").
If the mass is too light, vertical motion is too frequent to match the twist
but if the mass is too heavy the vertical motion is not frequent enough.

External horizontal Force (if that's what you want) is usually mostly
the flexing of the support rods. With too heavy a weight, the amplitude
of oscillation will be low (to NOT hit the floor); a slow frequency will make small variation in acceleration, so won't change the post flexure much
(what causes Work to be done by the post: not just F, but F dx !).
hope this helped

Last edited: Nov 20, 2005
3. Nov 20, 2005

### Atomos

I dont really understand how a slower frequency of the application of the sidways motion (i.e. bending of support) would prevent the pendulum motion. Even if it is slow, at certain masses, it will occur at such multiples of time that is adds to the amplitude of the side to side motion.

Last edited: Nov 20, 2005
4. Nov 20, 2005

### Atomos

And why would a greater mass cause the amplitude of the bending support to decrease?

5. Nov 20, 2005

### Atomos

bumpedy bump bump

6. Nov 20, 2005

### lightgrav

you have z(t) = A sin(wt) , with height variation 2A.

Now compute the acceleration function ...
what's the variation in the acceleration?
So what's the variation in the Force applied to the support?
Does it depend on angular frequency? does it depend on m?