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.) NA mass of 1 kg is attached to the end of a spring whose restoring force is 180 The mass is in a mediummm-The viscous resistance isSthat exerts a viscous resistance of 156 N when the mass has a velocity of 6proportional to the speed of the object.Suppose the spring is stretched 0.07 m beyond the its natural position and released. Let positivedisplacements indicate a stretched spring, and suppose that external vibrations act on the mass with aforce 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'snatural position, in m after t seconds. (Note: This spring-mass system is not "hanging", so there is nogravitational force included in the model.)u(t) =

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. 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) =

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.7: Applications

Problem 18EQ

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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.)