The model for the temperature of the object, T , after t minutes by using Newton’s law of Cooling where an object is heated to 100 ∘ C and it is left to cool in a room that has a temperature of 30 ∘ C and after 5 minutes, the temperature of the object is 80 ∘ C .
The model for the temperature of the object, T , after t minutes by using Newton’s law of Cooling where an object is heated to 100 ∘ C and it is left to cool in a room that has a temperature of 30 ∘ C and after 5 minutes, the temperature of the object is 80 ∘ C .
Solution Summary: The author calculates the temperature of the object, T, after t minutes by using Newton's law of Cooling.
To calculate: The model for the temperature of the object, T, after t minutes by using Newton’s law of Cooling where an object is heated to 100∘C and it is left to cool in a room that has a temperature of 30∘C and after 5 minutes, the temperature of the object is 80∘C.
(b)
To determine
To calculate: The temperature of the object after 20 minutes where an object is heated to 100∘C and it is left to cool in a room that has a temperature of 30∘C and after 5 minutes, the temperature of the object is 80∘C.
(c)
To determine
To calculate: The time at which the temperature of the object is 35∘C when an object is heated to 100∘C and it is left to cool in a room that has a temperature of 30∘C and after 5minutes, the temperature of the object is 80∘C.
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?
1. Solve the initial value problem:
y" -11y' + 30y = x³e6x
y(0) 11, y'(0) = 36
=
Chapter 3 Solutions
MyLab Math with Pearson eText -- Standalone Access Card -- for Precalculus (6th Edition)
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