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An object on a horizontal spring oscillates with a period of 1 s. If the object is suspended from...

Question:

An object on a horizontal spring oscillates with a period of 1 s. If the object is suspended from the spring vertically, by how much is the spring stretched from its natural length when the object is in equilibrium?

Spring-mass System:

The duration of motion of a spring-mass system does not depend on the orientation of the system, i.e., whether it is vertical or horizontal. When the vertical spring-mass system is in a steady-state, we can measure its deformation directly or we can determine it using Hooke's law. In the second case, you need the force constant of spring and the mass of the object. Mathematically:

{eq}x=\rm \dfrac{spring \ force}{force \ constant} {/eq}

where:

  • {eq}x {/eq} is the deformation of the spring

Answer and Explanation:

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Given data:

  • {eq}T=\rm 1 \ s {/eq} is the period of motion
  • {eq}k {/eq} is the spring constant of the spring
  • {eq}m {/eq} is the mass of an object
  • ...

See full answer below.


Learn more about this topic:

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Hooke's Law & the Spring Constant: Definition & Equation

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Chapter 4 / Lesson 19
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After watching this video, you will be able to explain what Hooke's Law is and use the equation for Hooke's Law to solve problems. A short quiz will follow.


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