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A mass m on the end of a spring oscillates with angular frequency (omega). The mass is removed,...

Question:

A mass {eq}m {/eq} on the end of a spring oscillates with angular frequency {eq}(\omega) {/eq}. The mass is removed, the spring is cut in two, and the mass is reattached. What is the new angular frequency?

Spring Constant of Springs Connected in Series and Parallel

Spring constant or the force constant of the spring can be defined as the force required to elongate or compress a spring by unit length. If a spring is stretched by x distance by applying a force F, its spring constant can be expressed as {eq}k = \dfrac { F } { x } {/eq}. Spring constant is expressed in Newtons per meter.

  • When n springs of spring constants {eq}k_1, \ \ k_2, \ \ k_3, \ \ ...... \ k_n {/eq} are connected in series, the inverse of the effective spring constant of the series combination can be expressed as {eq}\dfrac {1 } { k_s } = \dfrac{1 } { k_1 } + \dfrac { 1 } { k_2 } + \ ..... \ \dfrac { 1 } { k_n } {/eq}
  • When n springs of spring constants {eq}k_1, \ \ k_2, \ \ k_3, \ \ ...... \ k_n {/eq} are connected in parallel, the effective spring constant of the parallel combination can be expressed as {eq}k_p = k_1 + k_2 + \ ...... \ k_n {/eq}

Answer and Explanation:

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Given data

  • A mass m connected at the end of a spring oscillates with angular frequency {eq}\omega {/eq}
  • The mass is removed and the spring is cut...

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Practice Applying Spring Constant Formulas

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Chapter 17 / Lesson 11
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In this lesson, you'll have the chance to practice using the spring constant formula. The lesson includes four problems of medium difficulty involving a variety of real-life applications.


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