Four people sit in a car. The masses of the people are 50 kg, 57 kg, 63 kg, and 65 kg. The car's mass is 1020 kg. When the car drives over a bump, its springs cause an oscillation with a frequency of 2.90 Hz. What would the frequency be if only the 50-kg person were present?
I'm so lost over this.
Thank for any help
I'm so lost over this.
Thank for any help
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Basic equation
k= F/x
F/x = m w^2 ( w is the angular velocity = 2 pi() f or 2Pi()/T)
so if the spring constant k is the same then
w^2 is proportional to 1/m
or w is proportional to sqrt(1/m)
this means that w2/w1 = sqrt(m1/m2)
w2 = w1 * sqrt(m1/m2)
As w and f are proportional then it is just as true that
f2 = f1*sqrt(m1/m2)
now m1 = 1020 +50+57+63+65 = 1255Kg
and m2 = 1070
so f2= 2.90 * sqrt(1255/1070)
= 3.14 Hz
k= F/x
F/x = m w^2 ( w is the angular velocity = 2 pi() f or 2Pi()/T)
so if the spring constant k is the same then
w^2 is proportional to 1/m
or w is proportional to sqrt(1/m)
this means that w2/w1 = sqrt(m1/m2)
w2 = w1 * sqrt(m1/m2)
As w and f are proportional then it is just as true that
f2 = f1*sqrt(m1/m2)
now m1 = 1020 +50+57+63+65 = 1255Kg
and m2 = 1070
so f2= 2.90 * sqrt(1255/1070)
= 3.14 Hz