. A mass of 1 kg is attached to the end of a spring whose restoring force is 180 The mass is in a medium m m - The viscous resistance is S that exerts a viscous resistance of 156 N when the mass has a velocity of 6 proportional to the speed of the object. Suppose the spring is stretched 0.07 m beyond the its natural position and released. Let positive displacements indicate a stretched spring, and suppose that external vibrations act on the mass with a force of 7 sin(3t) N at time t seconds. Find an function to express the steady-state component of the object's displacement from the spring's natural position, in m after t seconds. (Note: This spring-mass system is not "hanging", so there is no gravitational force included in the model.) u(t) =
. A mass of 1 kg is attached to the end of a spring whose restoring force is 180 The mass is in a medium m m - The viscous resistance is S that exerts a viscous resistance of 156 N when the mass has a velocity of 6 proportional to the speed of the object. Suppose the spring is stretched 0.07 m beyond the its natural position and released. Let positive displacements indicate a stretched spring, and suppose that external vibrations act on the mass with a force of 7 sin(3t) N at time t seconds. Find an function to express the steady-state component of the object's displacement from the spring's natural position, in m after t seconds. (Note: This spring-mass system is not "hanging", so there is no gravitational force included in the model.) u(t) =
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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Question
A mass of 1 kgkg is attached to the end of a spring whose restoring force is 180 NmNm. The mass is in a medium that exerts a viscous resistance of 156 NN when the mass has a velocity of 6 msms. The viscous resistance is proportional to the speed of the object.
Suppose the spring is stretched 0.07 mm beyond the its natural position and released. Let positive displacements indicate a stretched spring, and suppose that external vibrations act on the mass with a force of 7sin(3t)7sin(3t) NN at time tt seconds.
Find an function to express the steady-state component of the object's displacement from the spring's natural position, in mm after tt seconds. (Note: This spring-mass system is not "hanging", so there is no gravitational force included in the model.)
![### Spring-Mass System with Damping and External Vibrations
#### Problem Description
A mass of \( 1 \, \text{kg} \) is attached to the end of a spring whose restoring force is \( 180 \, \frac{N}{m} \). The mass is in a medium that exerts a viscous resistance of \( 156 \, N \) when the mass has a velocity of \( 6 \, \frac{m}{s} \). The viscous resistance is proportional to the speed of the object.
Suppose the spring is stretched \( 0.07 \, \text{m} \) beyond its natural position and released. Let positive displacements indicate a stretched spring, and suppose that external vibrations act on the mass with a force of \( 7 \sin(3t) \, N \) at time \( t \) seconds.
#### Objective
Find a function to express the *steady-state component* of the object's displacement from the spring's natural position, in meters, after \( t \) seconds.
**Note:** This spring-mass system is not "hanging," so there is no gravitational force included in the model.
\[ u(t) = \boxed{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F22e84192-4b16-4dc2-817c-afb771201e2b%2F55f8cc66-05e6-45c1-8085-43273d394be2%2Fmhdu8x4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Spring-Mass System with Damping and External Vibrations
#### Problem Description
A mass of \( 1 \, \text{kg} \) is attached to the end of a spring whose restoring force is \( 180 \, \frac{N}{m} \). The mass is in a medium that exerts a viscous resistance of \( 156 \, N \) when the mass has a velocity of \( 6 \, \frac{m}{s} \). The viscous resistance is proportional to the speed of the object.
Suppose the spring is stretched \( 0.07 \, \text{m} \) beyond its natural position and released. Let positive displacements indicate a stretched spring, and suppose that external vibrations act on the mass with a force of \( 7 \sin(3t) \, N \) at time \( t \) seconds.
#### Objective
Find a function to express the *steady-state component* of the object's displacement from the spring's natural position, in meters, after \( t \) seconds.
**Note:** This spring-mass system is not "hanging," so there is no gravitational force included in the model.
\[ u(t) = \boxed{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \]
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