How Does Doubling the Springs Affect the Oscillation Period?

• map7s
In summary, the conversation discusses the use of a modified equation to solve for the period of a spring system with identical springs and a mass of 1.19 kg. The simplified equation, F=2kx, is used to determine the total force on the block and is then incorporated into the equation T=2pi*square root of m/(2k) to find the period.
map7s
There is a spring with one end attached to a wall and the other end attached to a mass of 1.19 kg. On the other side of the mass is another spring whose other end is attached to another wall. The springs are identical and have a spring constant value of 49.7 N/m. What is the period?

I drew out a picture and I know that I need to use the equation T=2pi*square root of mass/k but with some modifications to the k. At first I thought that, with the spring being identical on both sides, the spring force would cancel out, but obviously that was wrong. How would I be able to use a modified form of this equation to solve for the period?

There might be a simplification that would help. In the linear region, the spring force is just F=kx, where x is the displacement, regardless of whether it is compression or tension. If you displace the block to the right some distance, that is seen by one spring as compression and by the other as tension, right? What is the total force on the block from the 2 springs, expressed in terms of the value k and the displacement?...

Would it just be F=2kx ?

map7s said:
Would it just be F=2kx ?
Yep. So that simplifies working out the answer for the period, right?

So, would I have to use the equation T=2pi*square root of m/(2k) ?

map7s said:
So, would I have to use the equation T=2pi*square root of m/(2k) ?
That will do it.

1. What is the period of a mass on a spring?

The period of a mass on a spring refers to the amount of time it takes for the mass to complete one full oscillation, or back and forth motion, on the spring.

2. How is the period of a mass on a spring calculated?

The period of a mass on a spring can be calculated using the formula T = 2π√(m/k), where T is the period in seconds, m is the mass of the object in kilograms, and k is the spring constant in Newtons per meter.

3. What factors affect the period of a mass on a spring?

The period of a mass on a spring is affected by the mass of the object, the spring constant, and the amplitude, or maximum displacement, of the oscillation. It is also affected by external factors such as air resistance and friction.

4. How does the period of a mass on a spring change with different masses?

The period of a mass on a spring is directly proportional to the square root of the mass. This means that as the mass increases, the period also increases, but at a slower rate.

5. Can the period of a mass on a spring be changed by adjusting the spring's length?

No, the period of a mass on a spring is not affected by the length of the spring. It is only affected by the spring constant and the mass of the object attached to the spring.

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