# Trying to Calculate k, using Hooke's Law

• masterexploder
In summary, the position of a 49 g oscillating mass is given by x(t)=(1.8cm)cos12t, and the spring constant can be determined using the formula k=mg/x. However, since the problem does not provide information about the length of the spring or its equilibrium state, this formula cannot be used. Instead, one should consider the relationship between the spring constant and the amplitude of the oscillation, as well as any other relevant equations.
masterexploder

## Homework Statement

The position of a 49 g oscillating mass is given by x(t)=(1.8cm)cos12t, where t is in seconds.

k=mg/x

## The Attempt at a Solution

I've tried working this problem multiple different ways and it is just not working for me.
I used k= (.049*9.8)/.018
Is this correct with the information I've been given? I used up all my attempts and the solution is apparently
7.1 N/m...but I keep coming up with roughly 26.7 N/m

Hello ex master,
masterexploder said:
Is this correct with the information I've been given
It is not. One can stretch a spring wrt its equilibrium state, and then let go. The amount of stretch becomes the amplitude of the ensuing oscillation so it has little to do with the spring constant.
You have been given another bit of info that does have a relationship with the spring constant. Can you guess which bit ?

kx = mg answers the question "how much does the spring stretch when I add this mass". It is an equilibrium answer. The problem didn't tell you how long the spring was before you added mass, or for that matter how long the spring was after the mass was added. What you have is how the spring oscillates about the equilibrium point. Do you have any other equations or ideas that might apply?

Cutter Ketch said:
kx = mg answers the question "how much does the spring stretch when I add this mass
Yes, but even then that is only in a vertical context.
@masterexploder , there is nothing in the question about the spring being vertical. This could be happening on a smooth horizontal surface, so you have no basis for involving g.

Chestermiller

## What is Hooke's Law?

Hooke's Law is a scientific principle that states the force needed to extend or compress a spring is directly proportional to the distance the spring is stretched or compressed.

## What is k in Hooke's Law?

k, also known as the spring constant, is a numerical value that represents the stiffness of a spring. It is used to calculate the force required to stretch or compress a spring a certain distance.

## How do you calculate k using Hooke's Law?

To calculate k, you need to measure the force applied to the spring and the distance the spring is stretched or compressed. Then, divide the force by the distance to obtain the value of k.

## Why is it important to calculate k using Hooke's Law?

Calculating k is important because it allows us to understand the behavior of springs and how they respond to different forces. This knowledge is crucial in many fields, such as engineering, physics, and materials science.

## Are there any limitations to using Hooke's Law?

Yes, there are limitations to using Hooke's Law. It only applies to elastic materials, and the relationship between force and distance is only linear within a certain range. It also does not take into account factors such as temperature, material fatigue, and external forces.

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