The average water level in a retention pond is 6.8 ft. During a time of drought, the water level decreases at a rate of 3 in./day. a. Write a linear function W that represents the water level W t in ft t days after a drought begins. b. Evaluate W 20 and interpret the meaning in the context of this problem.
The average water level in a retention pond is 6.8 ft. During a time of drought, the water level decreases at a rate of 3 in./day. a. Write a linear function W that represents the water level W t in ft t days after a drought begins. b. Evaluate W 20 and interpret the meaning in the context of this problem.
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
=
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.