For an oscillating air-track glider (Figure 1) , the force constant of the sprin

Question

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.

SET UP AND SOLVE All the necessary relationships are contained in the equations for , f, and T. For ,

=km=200N/m0.50kg=200(kgm/s2)/m0.50kg=20s1

and for f and T,

f=2=3.2Hz,T=1f=0.31s

REFLECT The angular frequency is not directly proportional to the force constant, as one might naively guess. To double the value of we would have to increase k by a factor of 4.

PROBLEM:

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 to two significant figures.

Explanation / Answer

angular frequency w = sqrt(k/m)

w = sqrt(200/0.5) = 20 rad/s

frequency f = w/2pi = 20/(2pi) = 3.2 Hz

time period T = 1/f = 0.31 s

+++++++++

for time period T = 2 s

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

T = 2*pi*sqrt(m/200)

2 = 2*pi*sqrt(m/200)

m = 20.3 kg <<<<------answer

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