The function F of v if the actual frequency of sound emitted by the ambulance is 560 H z when an ambulance is moving toward an observer and the frequency of a sound relative to an observer is given by F v = f a s 0 s 0 − v , where f a is the actual frequency of the sound at the source, s 0 is the speed of the sound in air 772.4 mph , and v is the speed at which the source of sound is moving toward the observer.
The function F of v if the actual frequency of sound emitted by the ambulance is 560 H z when an ambulance is moving toward an observer and the frequency of a sound relative to an observer is given by F v = f a s 0 s 0 − v , where f a is the actual frequency of the sound at the source, s 0 is the speed of the sound in air 772.4 mph , and v is the speed at which the source of sound is moving toward the observer.
Solution Summary: The author explains the cost function F of v if the actual frequency of sound emitted by the ambulance is 560Hz.
The function F of v if the actual frequency of sound emitted by the ambulance is 560Hz when an ambulance is moving toward an observer and the frequency of a sound relative to an observer is given by Fv=fas0s0−v , where fa is the actual frequency of the sound at the source, s0 is the speed of the sound in air 772.4mph , and v is the speed at which the source of sound is moving toward the observer.
(b)
To determine
To graph: The sketch of a function given by Fv=560772.4772.4−v on the window 0,1000,100by0,5000,1000 .
(c)
To determine
The effect of the frequency of sound when the speed of the ambulance increases.
2. Consider the following:
Prove that x, x2, and 1/x are the solutions to the homogeneous equation
corresponding to x³y"" + x²y" + 2xy' + 2y = 2x4.
b. use variation of parameters to find a particular solution and complete the general
solution to the differential equation. I am interested in process. You may use a
computer for integration, finding determinants and doing Kramer's.
3. A spring is stretched 6 in. by a mass that weighs 8 lb. The mass is attached to a dashpot
mechanism that has a damping constant of 0.25 lb-sec./ft. and is acted on by an external
force of 4 cos 2t lb.
a. Set-up the differential equation and initial value problem for the system.
b. Write the function in phase-amplitude form.
C.
Determine the transient solution to the system. Show your work.
d. Determine the steady state of this system. Show your work.
e.
Is the system underdamped, overdamped or critically damped? Explain what this
means for the system.
4. Suppose that you have a circuit with a resistance of 20, inductance of 14 H and a
capacitance of 11 F. An EMF with equation of E(t) = 6 cos 4t supplies a continuous charge
60
to the circuit. Suppose that the q(0)= 8 V and the q'(0)=7. Use this information to answer the
following questions
a. Find the function that models the charge of this circuit.
b. Is the circuit underdamped, overdamped or critically damped?
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