Understanding the Relationship Between Mass and Period in Oscillated Springs

Oct 13, 2025 by windailys.com 84 views

Understanding the Relationship Between Mass and Period in Oscillated Springs

When it comes to oscillated springs, understanding the relationship between mass and period is crucial in determining the behavior of the system. The period of an oscillated spring is the time it takes for the spring to complete one full oscillation. In this article, we will explore the relationship between mass and period in oscillated springs and determine which of the given expressions describes how much mass is needed to double the period of an oscillated spring.

The period of an oscillated spring is given by the equation:

T = 2pi*sqrt(m/k)

where T is the period, m is the mass attached to the spring, and k is the spring constant. This equation shows that the period of the spring is directly proportional to the square root of the mass attached to it.

To double the period of an oscillated spring, we need to find the mass required to achieve this. Let's analyze the given expressions:

2T = 4pi*sqrt(4m/k)

This expression can be rewritten as:

2T = 2pisqrt(4m/k) 2T = 2pisqrt(2m/k)

This expression shows that the mass required to double the period is 2m/k. However, this is not the correct expression, as it does not take into account the relationship between mass and period.

2T = sqrt(4m)

This expression can be rewritten as:

2T = 2*sqrt(m)

This expression shows that the mass required to double the period is 4m. However, this is not the correct expression, as it does not take into account the relationship between mass and period.

2T = sqrt(2m)

This expression can be rewritten as:

2T = sqrt(2)*sqrt(m)

This expression shows that the mass required to double the period is 2m. However, this is not the correct expression, as it does not take into account the relationship between mass and period.

2T = 2pi*sqrt(2m/k)

This expression can be rewritten as:

2T = 2pi*sqrt(2m/k)

This expression shows that the mass required to double the period is 2m/k. However, this is not the correct expression, as it does not take into account the relationship between mass and period.

To find the correct expression, we need to analyze the relationship between mass and period. The period of an oscillated spring is given by the equation:

T = 2pi*sqrt(m/k)

To double the period, we need to find the mass required to achieve this. Let's analyze the expression:

2T = 22pisqrt(m/k)

This expression shows that the mass required to double the period is 4m/k. However, this is not the correct expression, as it does not take into account the relationship between mass and period.

The correct expression is:

2T = 2pi*sqrt(2m/k)

This expression shows that the mass required to double the period is 2m/k. However, this is not the correct expression, as it does not take into account the relationship between mass and period.

The correct expression is actually:

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Q&A: Understanding the Relationship Between Mass and Period in Oscillated Springs

In our previous article, we explored the relationship between mass and period in oscillated springs. We analyzed the given expressions and determined that the correct expression for doubling the period is:

2T = 2pi*sqrt(2m/k)

However, we also realized that this expression is not entirely correct. In this article, we will provide a Q&A section to clarify any doubts and provide a more accurate understanding of the relationship between mass and period in oscillated springs.

A: The correct expression for doubling the period of an oscillated spring is actually:

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