Vertical oscillations question

In summary, the amplitude of the subsequent oscillations in a vertical spring system will be the distance between the new equilibrium point and the height at which it was held before it was released. The force of gravity only determines the equilibrium point and does not affect the motion.
  • #1
maccha
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I have a question about vertical oscillations. If a vertical spring, fixed at one end with a mass attached to the other and held so that the spring is not stretched.. is then released, will the amplitude of the subsequent oscillations be the distance between the new equilibrium point (of mass and spring system) and the height at which it was held before it was released? If that makes any sense.

For example, in class we've talked about how the force of gravity only plays a role in determining the equilibrium point and does not affect the actual motion. All the problems we've covered have said "the spring is stretched x meters from the equilibrium point"- so you know that's the amplitude. So I'm wondering if you drop a spring from a certain height above its equilibrium point, will that height be the height of the subsequent oscillations?
 
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  • #2
Yes, the height at which the spring was held before it was released will be the amplitude of the subsequent oscillations. The force of gravity does not affect the motion of the spring, but it does determine the equilibrium point. The difference between the new equilibrium point and the height at which it was held before it was released will be the amplitude of the oscillations.
 
  • #3


Yes, the amplitude of the subsequent oscillations will be equal to the distance between the new equilibrium point and the height at which the spring was held before it was released. This is because the initial release of the spring will cause it to oscillate around the new equilibrium point, with a maximum displacement equal to the initial distance from the equilibrium point. The force of gravity does not affect the motion of the spring, but it does determine the new equilibrium point. Therefore, the height at which the spring was held before being released will be the same as the amplitude of the subsequent oscillations. This is also true for situations where the spring is stretched from the equilibrium point, as the amplitude will still be equal to the distance between the new equilibrium point and the point where the spring was initially stretched.
 

1. What are vertical oscillations?

Vertical oscillations refer to the up and down motion of an object, often caused by a force acting on it. It can also be described as the back and forth motion of an object along a vertical axis.

2. What factors affect the vertical oscillations of an object?

The main factors that affect the vertical oscillations of an object are its mass, elasticity, and the force acting on it. The greater the mass and elasticity of an object, the slower and larger its vertical oscillations will be. The force acting on the object can also change the amplitude and frequency of its oscillations.

3. What is the difference between simple harmonic motion and vertical oscillations?

Simple harmonic motion is a type of oscillating motion where an object moves back and forth in a regular pattern, while vertical oscillations specifically refer to the up and down motion of an object. All vertical oscillations are considered simple harmonic motion, but not all simple harmonic motion is vertical oscillation.

4. How can the period of vertical oscillations be calculated?

The period, or the time it takes for one complete oscillation, can be calculated using the formula T=2π√(m/k), where T is the period, m is the mass of the object, and k is the spring constant or elasticity of the object. This formula assumes that the oscillations are simple harmonic and that there is no damping or external forces acting on the object.

5. How can vertical oscillations be applied in real-world situations?

Vertical oscillations have many practical applications, such as in pendulum clocks, spring scales, and suspension systems in vehicles. They are also used in various engineering and scientific fields, such as earthquake monitoring and studying the behavior of buildings and bridges during seismic events.

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