# What is the Period of Oscillation for Two Masses Connected by a Spring?

• WorkIsNotAVec
In summary, the problem is to find the period of oscillation for a system consisting of two masses attached by an ideal spring with a spring constant of 0.5 N/m. The masses are 100 g and 200 g, and the system is on a frictionless horizontal surface. The equations used are F=-kx, x(t)=Acos(wt - \phi), and Fnet=ma. After initial compression/stretch, each spring is displaced by x and the total displacement is 2x. The equation of motion for each mass is x1(t) = xcos(w1t) and x2(t) = xcos(w2t). The individual angular frequencies w1 and w2 can be found,
WorkIsNotAVec

## Homework Statement

This is my first time using this forum so I'll try to start this off right.
The question is this : Two masses, one 100 g and the other 200 g are attached via an ideal spring with spring constant k = 0.5 N/m. The system is slid along a frictionless horizontal surface, find the period of oscillation.

## Homework Equations

F=-kx
x(t)=Acos(wt - $$\phi$$)
Fnet=ma
Not sure what else.

## The Attempt at a Solution

I know that after the initial compression/stretch each spring will be displaced by x, and the total displacement will have been 2x. So the equation of motions for the two masses would be:
x1(t) = xcos(w1t)
x2(t) = xcos(w2t)
And I can find the individual angular frequencies w1 and w2, but I don't understand how to go on from here to find the frequency of it as a whole.

I was thinking that I could find the period of each mass and then add them together, but then I would have to account for the phase difference between the two masses. Any help is greatly appreciated!

## 1. How does the spring behave when two masses are attached to it?

When two masses are attached to one spring, the spring will stretch and compress according to the combined weight of the two masses. This means that the spring will behave differently than if only one mass was attached, as it will stretch further and compress more.

## 2. What happens to the period of oscillation when two masses are attached to the spring?

The period of oscillation, or the time it takes for one complete cycle of the spring's movement, is affected by the combined weight of the two masses. The heavier the masses, the longer the period will be. However, the spring constant and length of the spring will also play a role in determining the period.

## 3. Can two different masses be attached to the spring and still exhibit harmonic motion?

Yes, as long as the two masses are relatively close in weight and the spring is not stretched beyond its elastic limit. The masses will still exhibit harmonic motion, but the period and amplitude may be different compared to two identical masses attached.

## 4. How does the position of the two masses affect the spring's behavior?

The position of the two masses on the spring will affect the equilibrium position and amplitude of the spring's oscillations. If the masses are not evenly distributed, the equilibrium position will be closer to the heavier mass. The amplitude will also be affected, as the heavier mass will cause the spring to stretch more and compress more, resulting in larger oscillations.

## 5. Can the spring's behavior be affected by external factors when two masses are attached?

Yes, external factors such as air resistance or friction can affect the spring's behavior when two masses are attached. These factors can alter the period and amplitude of the oscillations, making the spring's behavior less predictable. It is important to control for these external factors in experiments involving 2 masses with one spring to get accurate results.

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