# 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:

Become a Study.com member to unlock this answer! Create your account

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...

See full answer below.

#### Learn more about this topic: Practice Applying Spring Constant Formulas

from

Chapter 17 / Lesson 11
3.1K

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.