An interactive introduction to MATLAB

82 additional exercises

whereMis the molar mass of the gas inkg/mol,R=8.31 J/mol K

is the gas constant,T is the temperature inK, andvis the molecules

speed inm/s. Make a 3dsurface plot ofP(v)as a function ofvand

T for 06 v 6 1000 m/sand 706 T 6 320 Kfor oxygen (molar mass

M=0.032 kg/mol).

18. 3D plotting
    An RLC circuit with an alternating voltage source is shown in Figure 24.
    The source voltagevsis given byvs=vmsin(ωdt)whereωd=2πfdis

+ V

• s = vmsin(wdt)

R

C

L

Figure 24: An RLC circuit with an alternating voltage source

whichfdis the driving frequency. The amplitude of the currentIin the

circuit is given by:

I=√ vm

R^2 +

(

ωdL−ω^1 dC

) 2 ,

whereRandCare the resistance of the resistor and the capacitance of

the capacitor, respectively. For the circuit in Figure 24C= 15 × 10 −^6 F,

L= 240 × 10 −^3 H, andvm=24 V.

a)Make a 3dsurface plot of the currentI(zaxis) as a function of

ωd(xaxis) for 606 f 6 110 Hz, and a function ofR(yaxis) for

106 R 6 40 Ω.

b) Rotate the plot into thex−zplane. Estimate the natural frequency

of the circuit (the frequency at whichIis maximum). Compare the

estimate with the calculated value of1/(2π

√

LC).