c. Solve the initial value problem for y(t). y(t) = 1/4(cos(8t)-cos(10t)) help (formulas) d. Plot the solution and determine the maximum excursion from equilibrium made by the object on the time interval 0
c. Solve the initial value problem for y(t). y(t) = 1/4(cos(8t)-cos(10t)) help (formulas) d. Plot the solution and determine the maximum excursion from equilibrium made by the object on the time interval 0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![The image displays a problem involving a mass-spring system and the steps to solve it.
**Problem Statement:**
A 10-kilogram object is suspended from the end of a vertically hanging spring, stretching the spring 9.8 centimeters. At time \( t = 0 \), the system is disturbed by the force \( F(t) = 90 \cos(10t) \). The force \( F(t) \) is in Newtons, acting positively downward, and time is measured in seconds.
**Tasks:**
- **a. Determine the spring constant \( k \):**
\( k = 1000 \) Newtons per meter
- **b. Formulate the initial value problem for \( y(t) \), the displacement of the object:**
**Differential equation:**
\[
y'' + 100y = 9 \cos(10t)
\]
**Initial conditions:**
\[
y(0) = 0 \quad \text{and} \quad y'(0) = 0
\]
- **c. Solve the initial value problem for \( y(t) \):**
Attempted solution:
\[
y(t) = \frac{1}{4} (\cos(8t) - \cos(10t))
\]
(The attempted solution is marked incorrect)
- **d. Determine the maximum excursion from equilibrium:**
\[\text{Maximum excursion} = 0.58 \text{ meters}\]
(Again, the entered value is marked incorrect)
**Feedback:**
The system notes that at least one of the answers provided is incorrect, notably the solution for \( y(t) \) and the maximum excursion value.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdf1d0bb8-6fc4-423e-9784-469bf31e55bd%2Ff8ba03fe-766d-49a5-982e-789d65510025%2Ft5nczm8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image displays a problem involving a mass-spring system and the steps to solve it.
**Problem Statement:**
A 10-kilogram object is suspended from the end of a vertically hanging spring, stretching the spring 9.8 centimeters. At time \( t = 0 \), the system is disturbed by the force \( F(t) = 90 \cos(10t) \). The force \( F(t) \) is in Newtons, acting positively downward, and time is measured in seconds.
**Tasks:**
- **a. Determine the spring constant \( k \):**
\( k = 1000 \) Newtons per meter
- **b. Formulate the initial value problem for \( y(t) \), the displacement of the object:**
**Differential equation:**
\[
y'' + 100y = 9 \cos(10t)
\]
**Initial conditions:**
\[
y(0) = 0 \quad \text{and} \quad y'(0) = 0
\]
- **c. Solve the initial value problem for \( y(t) \):**
Attempted solution:
\[
y(t) = \frac{1}{4} (\cos(8t) - \cos(10t))
\]
(The attempted solution is marked incorrect)
- **d. Determine the maximum excursion from equilibrium:**
\[\text{Maximum excursion} = 0.58 \text{ meters}\]
(Again, the entered value is marked incorrect)
**Feedback:**
The system notes that at least one of the answers provided is incorrect, notably the solution for \( y(t) \) and the maximum excursion value.
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