Learning object 1
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The document describes two horizontal mass-spring systems (A and B) where the mass of A is twice that of B and the spring constant of B is 3 times that of A, with equal rest lengths. To calculate the period, the equations T = 2π sqrt(m/k) is used for each system. For system A, the period is T = 2π sqrt(2) and for system B it is T = 2π sqrt(1/3). By dividing the periods, the document determines that the period of A is 2.45 times longer than the period of B.
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Learning object 1
- 1. Learning Object 1 Lyndon Won Spring Systems Question: There are 2 horizontal mass-spring systems (shown below). The mass of A is twice that of B. The spring constant of B is 3 times that of A. The rest lengths are equal. How does the period of A compare that of B (how many times larger is one compared to the other)? Diagram A Diagram B
- 2. Learning Object 1 Lyndon Won Spring Systems Solution: The equation for period is T = 2π sqrt(m/k) First, plug in the values for A: T = 2π sqrt(2m/k) Next, input values for B: T = 2π sqrt(m/3k) Since both use the variables m and k, they can be ignored Therefore the equation for A can be simplified to: T = 2π sqrt(2/1) = 2π sqrt(2) And B: T = 2π sqrt(1/3) Then to find how many times larger A is then B: 2π sqrt(2) = sqrt(2) = 2.45 2π sqrt(1/3) sqrt(1/3) Therefore the period of A is 2.45 times longer than the period of B