For an oscillating air-track glider (Figure 1), the force constant of the spring is k=200N/m and the glider mass is m=0.50kg. Now let's find the angular frequency, frequency, and period of the glider's motion. a)suppose we could "tune" this system by varying the mass. What mass would be required for a period of 2.0 s? Express your answer in kilograms.

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Chapter1: Units, Trigonometry. And Vectors
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For an oscillating air-track glider (Figure 1), the force constant of the spring is k=200N/m and the glider mass is m=0.50kg. Now let's find the angular frequency, frequency, and period of the glider's motion.

a)suppose we could "tune" this system by varying the mass. What mass would be required for a period of 2.0 s?

Express your answer in kilograms.
 
 
k = 200 N/m
m = 0.50 kg
x = 0
Transcribed Image Text:k = 200 N/m m = 0.50 kg x = 0
SOLUTION
SET UP AND SOLVE All the necessary relationships are contained in the equations for w, f, and T. For w,
200 N/m
200 (kg · m/s2)/m
W =
= 20 s-1
0.50 kg
0.50 kg
m
and for f and T,
= 3.2 Hz, T=
1
= 0.31 s
REFLECT The angular frequency is not directly proportional to the force constant, as one might naively guess. To double the
value of w we would have to increase k by a factor of 4.
Transcribed Image Text:SOLUTION SET UP AND SOLVE All the necessary relationships are contained in the equations for w, f, and T. For w, 200 N/m 200 (kg · m/s2)/m W = = 20 s-1 0.50 kg 0.50 kg m and for f and T, = 3.2 Hz, T= 1 = 0.31 s REFLECT The angular frequency is not directly proportional to the force constant, as one might naively guess. To double the value of w we would have to increase k by a factor of 4.
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