Pendulum Motion II. The motion of a simple pendulum as a function oftime is described by the following second-order differential equation:d'080 = 0+di?'Lwhere the terms in the equation are as defined in the preceding problem.Generate a table of angle of displacement as a function of time from / 0 to t= 2 seconds, with 0-10° and d@dt - 0 at /= 0.Liquid Flow. A cylindrical tank of diameter D is filled with water to aheight h. Water is allowed to flow out of the tank through a hole of diameterd in the bottom of the tank. The differential equation describing the height ofwater in the tank as a function of time isd?/2ghdhdtD2where g is the acceleration due to gravity. Produce a plot of height of waterin the tank as a function of time for D = 10 ft, d = 6 in and ho = 30 ft.Compare your results with the analytical solution h=h, - kt/2, wherek = (d² /D')/2g. hnen'tFor 1 mole of a gas, the van der Waals equation iswhere R is the gas constant (0.0821 L atm K mol ') and 7 is the Kelvintemperature 1The constants a and h are constants particular to a given gasand correct for the attractive forces between gas molecules, and for thevolume occupied by the gas molecules, respectively. For methane (CH), theconstants are a 2.253 L'atm and b4.278 x 10 L. Using the rearrangedform of the van der Waals equationRTV -b v?calculate the pressure of 1 mole of methane as a function of container volume0°C (273 K) at suitable volumes from 22.4 L to 0.05 L. Use one of theatcustom functions described in this chapter to calculate the first and secondderivatives of the P-V relationship. Compare with the exact expressionsdPRT2adV(v - b)?v3d? P2RT6adv? (V -b)

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Elements Of Electromagnetics

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Author:Sadiku, Matthew N. O.

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Conservation of Energy

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Pendulum Motion II. The motion of a simple pendulum as a function of
time is described by the following second-order differential equation:
d'0
80 = 0
+
di?'L
where the terms in the equation are as defined in the preceding problem.
Generate a table of angle of displacement as a function of time from / 0 to t
= 2 seconds, with 0-10° and d@dt - 0 at /= 0.
Liquid Flow. A cylindrical tank of diameter D is filled with water to a
height h. Water is allowed to flow out of the tank through a hole of diameter
d in the bottom of the tank. The differential equation describing the height of
water in the tank as a function of time is
d?
/2gh
dh
dt
D2
where g is the acceleration due to gravity. Produce a plot of height of water
in the tank as a function of time for D = 10 ft, d = 6 in and ho = 30 ft.
Compare your results with the analytical solution h=h, - kt/2, where
k = (d² /D')/2g.

hnen't
For 1 mole of a gas, the van der Waals equation is
where R is the gas constant (0.0821 L atm K mol ') and 7 is the Kelvin
temperature 1The constants a and h are constants particular to a given gas
and correct for the attractive forces between gas molecules, and for the
volume occupied by the gas molecules, respectively. For methane (CH), the
constants are a 2.253 L'atm and b4.278 x 10 L. Using the rearranged
form of the van der Waals equation
RT
V -b v?
calculate the pressure of 1 mole of methane as a function of container volume
0°C (273 K) at suitable volumes from 22.4 L to 0.05 L. Use one of the
at
custom functions described in this chapter to calculate the first and second
derivatives of the P-V relationship. Compare with the exact expressions
dP
RT
2a
dV
(v - b)?v3
d? P
2RT
6a
dv? (V -b)

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