# Springs

## Calculations of objects on springs exhibiting simple harmonic motion.

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That Shaky Bed!!

### What is it that makes a bed go up and down when we jump on one?

The spring system on a bed. [Figure1]

A spring is one type of physical system that exhibit oscillatory motion. It works when a force is exerted on the system. They are unique in that they have a spring stiffness constant k, and when you divide it by the mass and take the square root, you would have angular velocity. Hence,  = √k/m. However, like all oscillatory systems,  = 2f and T = 1/f.

There are many everyday objects which use a spring system. For example, a bed has a spring system underneath the mattress, which is why we move up and down when we jump on one. In other words, the spring system is exerting a force back on us whenever we put our weight on it.

### Creative Applications

1. What is the importance of having a spring system on beds?

2. Calculate the frequency of the spring system of the bed given that the spring has a spring constant of 500 N/m and a mass of 4 kg.

3. Why do you think that there are weight restrictions on beds?

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