Exercise 2.4.6: Suppose you wish to measure the friction a mass of 0.1 kg experiences as it slides along a floor (you wish to fi

Answer:

b = 0.6487 kg / s

Explanation:

In the context of oscillatory motion, friction is related to velocity,

               fr = - b v

where b represents the friction coefficient.

Upon solving the equation, the angular velocity is represented as

               w² = k / m - (b / 2m)²

In this case, we're given an angular frequency w = 1Hz, the mass m = 0.1 kg, and the spring constant k = 5 N / m. This allows us to derive the friction coefficient.

Let’s denote

               w₀² = k / m

               w² = w₀² - b² / 4m²

               b² = (w₀² -w²) 4 m²

Now, let's calculate the angular frequencies.

             w₀² = 5 / 0.1

             w₀² = 50

             w = 2π f

             w = 2π 1

             w = 6.2832 rad / s

Substituting values yields

               b² = (50 - 6.2832²) 4 0.1²

               b = √ 0.42086

                b = 0.6487 kg / s