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1. A mass spring system has a mass of 1kg, a damping constant of 7 Ns/m and a spring constant of 10 N/m. The mass is initially sitting at rest at the equilibrium point. Starting at t = 0, an external force of 120N is applied to the mass in the positive direction. (That is - the force is stretching the spring) This external force stops at t = 0.5, after which there is no external force. a. Write a piecewise-defined formula for the external force Fext (t) as a function of t. Then calculate its Laplace transform L{Fext (t)} (You will need this later) b. Write the initial value problem describing the situation. You can leave the external force written as Fext (t), but understand that it is the piecewise-defined function from part a. C. Solve the initial value problem from part a by taking the Laplace transform of both sides.

1. A mass spring system has a mass of 1kg, a damping constant of 7 Ns/m and a spring constant of 10 N/m. The mass is initially sitting at rest at the equilibrium point. Starting at t = 0, an external force of 120N is applied to the mass in the positive direction. (That is - the force is stretching the spring) This external force stops at t = 0.5, after which there is no external force. a. Write a piecewise-defined formula for the external force Fext (t) as a function of t. Then calculate its Laplace transform L{Fext (t)} (You will need this later) b. Write the initial value problem describing the situation. You can leave the external force written as Fext (t), but understand that it is the piecewise-defined function from part a. C. Solve the initial value problem from part a by taking the Laplace transform of both sides.

Linear Algebra: A Modern Introduction
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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1. A mass spring system has a mass of 1kg, a damping constant of 7 Ns/m and a spring constant of 10 N/m. The mass is initially sitting at rest at the equilibrium point. Starting at t = 0, an external force of 120N is applied to the mass in the positive direction. (That is - the force is stretching the spring) This external force stops at t = 0.5, after which there is no external force. a. Write a piecewise-defined formula for the external force Fext (t) as a function of t. Then calculate its Laplace transform L{Fext (t)} (You will need this later) b. Write the initial value problem describing the situation. You can leave the external force written as Fext (t), but understand that it is the piecewise-defined function from part a. C. Solve the initial value problem from part a by taking the Laplace transform of both sides.
Transcribed Image Text:1. A mass spring system has a mass of 1kg, a damping constant of 7 Ns/m and a spring constant of 10 N/m. The mass is initially sitting at rest at the equilibrium point. Starting at t = 0, an external force of 120N is applied to the mass in the positive direction. (That is - the force is stretching the spring) This external force stops at t = 0.5, after which there is no external force. a. Write a piecewise-defined formula for the external force Fext (t) as a function of t. Then calculate its Laplace transform L{Fext (t)} (You will need this later) b. Write the initial value problem describing the situation. You can leave the external force written as Fext (t), but understand that it is the piecewise-defined function from part a. C. Solve the initial value problem from part a by taking the Laplace transform of both sides.
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