# How do you compute the force constant of a spring? How do you find the time period of one...

## Question:

How do you compute the force constant of a spring?

How do you find the time period of one complete cycle of vibration?

## Spring:

Spring is an elastic member used to absorb the vibrations caused by an oscillating system, unbalanced system, etc. The number of vibrations absorbed by a spring in a unit of time defines its frequency.

If {eq}(F) {/eq} is the external force applied to the spring to stretch or compress it by a distance {eq}(x) {/eq} from its unstretched or initial position, we can compute the force by using Hooke's law which is expressed as follow:

{eq}\begin{align} F&=kx\\[0.3 cm] k&=\boxed{\dfrac{F}{x}} \end{align} {/eq}

Where

• k is the force constant of the spring

The time period of one complete cycle of vibration is expressed by the following equation:

{eq}\boxed{T=2\pi\sqrt{\dfrac{m}{k}}} {/eq}

Where

• m is the mass attached to the spring
• k is the force constant of the spring Practice Applying Spring Constant Formulas

from

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.