1. Suppose you place a 20.0-g mass on the end of a spring and end of the spring

Question

1. Suppose you place a 20.0-g mass on the end of a spring and end of the spring moves from a position 0.462m above the table to a position 0.370m above the table. What is the spring constant of the spring? (Show your work)

2. Suppose your spring has a mass of 11.4 g, your weight holder has a mass of 2.8 g, and you place a 15.0-g mass on the weight holder. What is the value for the effective mass? (Show your work)

3. Suppose you pull down on the mass from Question 2, set the system into oscillation and find that the system has a period of oscillation equal to 0.94 s. Calculate the spring constant using the effective mass from Question 2 and the period of oscillation. (Show your work)

Explanation / Answer

(1) Spring constant, k = mg/x = 0.02 * 9.81 / (0.462 - 0.370) = 2.13 N/m

(2) Effective mass of spring, mes = ms/3 = 11.4/3 = 3.8 g

[Reference: https://en.wikipedia.org/wiki/Effective_mass_(spring%E2%80%93mass_system)]

Hence, total effective mass, meff = (3.8 + 2.8 + 15) g = 21.6 g

(3) T = 2(meff/k)1/2 = 0.94

=> spring constant, k = meff (T/2)2 = 21.6 * 0.942 / 2 = 0.97 N/m

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