Answer:
The height of the water column = 1.62405
× 10⁻¹ m
Explanation:
The air cavity in the Coke bottle = 0.220 m deep
The fundamental (frequency) it plays when water is added to shorten the column and it is blown across the top, f = 528 Hz
The given speed of sound in air, v = 343 m/s
We note that the air cavity in the coke bottle is equivalent to a tube closed at one end
The fundamental frequency for a tube closed at one end, 'f', is given as follows;
f = v/(4·L) = v/λ
Where;
L = The height of the water column
λ = The wavelength of the wave
∴ 4·L = v/f = (343 m/s)/(528 Hz) = 0.6496
m
∴ L = 0.6496
m/4 = 0.162405
m
The height of the water column = 1.62405
× 10⁻¹ m.
Answer:
u" + 40u' + 49u = 2 sin(t/6)
upp + 40up + 49u = 2 sin(t/6)
Explanation:
Step 1: Data given
mass = 5 kg
L = 20 cm = 0.2 m
F = 10 sin(t/6)N
Fd(t) = - 6 N
u(0) = 0.03 m/s
u(0) = 0
u'(0) = 3 cm/s
Step 2:
ω =kL
k = ω/L = m*g /L = (5*9.8)/0.2 = 245 kg/s²
Since Fd(t) = -γu'(t) we know:
γ =- Fd(t) / u'(t) = 6N/ 0.03 m/s = 200 Ns/m
The initial value problem which describes the motion of the mass is given by
5u" + 200u' + 245u = 10 sin(t/6) u(0) = 0 ; u'(0) = 0.03
This is equivalent to:
u" + 40u' + 49u = 2 sin(t/6) u(0) = 0 ; u'(0) = 0.03
upp + 40up + 49u = 2 sin(t/6)
With u in m and t in s
Can you please include the statement or the model?
Explanation:
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Answer:
<h3>n(F) = 4</h3>
Explanation:
Cardinality of a set is the number of elements in that set. Given the set.
F= {mango, apple, banana, orange), we are to determine the cardinality of the set i.e the amount of fruit present in the set. Cardinality of the set F is represented as n(F).
Since there are 4 different fruit in the given set F, hence the cardinality of the set F is n(F) = 4