u" + 2u' + 10u = kg(t), u(0) = 0, u'(0) = 0, where g(t) = us(t) – us(t) and k> 0 is a parameter. a) Sketch the graph of the forcing function on an appropriate interval. 0.8 0.6 0.4 0.2 5) Solve the initial value problem. VOTE: Denote the two Heaviside functions by uc(t) and ua(t). Indicate separately he values of c and d knowing that c is the minimum of the two values. (t):
u" + 2u' + 10u = kg(t), u(0) = 0, u'(0) = 0, where g(t) = us(t) – us(t) and k> 0 is a parameter. a) Sketch the graph of the forcing function on an appropriate interval. 0.8 0.6 0.4 0.2 5) Solve the initial value problem. VOTE: Denote the two Heaviside functions by uc(t) and ua(t). Indicate separately he values of c and d knowing that c is the minimum of the two values. (t):
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question

Transcribed Image Text:A certain spring-mass system satisfies the initial value problem
u" + 2u' + 10u =
kg(t), u(0) = 0, u'(0) = 0,
where g(t) = uz(t) – us (t) and k > 0 is a parameter.
a) Sketch the graph of the forcing function on an appropriate interval.
0.8
0.6
0.4
0.2
1
4
b) Solve the initial value problem.
NOTE: Denote the two Heaviside functions by uc(t) and ua(t). Indicate separately
the values of c and d knowing that c is the minimum of the two values.
u(t) =

Transcribed Image Text:where c =
and d
1
c) Use a graphing utility to plot the solution for k
, k = 1, and
2'
k = 2. Describe the principal features of the solution and how they
depend on k.
In all cases the plot will be zero for 0 <t < ·
For
くtく
the plot will be the system
2
response to a step input of magnitude k.
When k increases the amplitude increases.
d) Use a graphing utility to find, to two decimal places, the smallest
value of k for which the solution u(t) reaches the value 1.
k = 2
e) Suppose k = 2. Use a graphing utility to find the time T, to two
decimal places, after which |u(t)| < 0.1 for all t> T.
312
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 5 steps with 5 images

Recommended textbooks for you

Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated

Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY

Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated

Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY

Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,

