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Problem 1 (Discontinuous Forcing). Suppose we have an undamped spring-mass system, where a 0.3 kg mass is attached to a spring with spring constant 30 N/m. At t = 0, the mass is disturbed from rest by an oscillating motor, which supplies a force of 3 cos 9.2t N to the system. After 10 seconds, the motor is switched off. We can model the forcing with the discontinuous function 3 cos 9.2t if 0 < t < 10 f(t) = %3D if t > 10. (a) Write down the initial value problem that describes this spring-mass system. (b) Solve the IVP from part (a) and express your answer as a piecewise function. Hint: First solve the IVP for 0 < t < 10, then for t > 10, and combine the two answers. Make sure the resulting function is differentiable at t = 10 (i.e. the functions and their derivatives must match up there). %3D

Problem 1 (Discontinuous Forcing). Suppose we have an undamped spring-mass system, where a 0.3 kg mass is attached to a spring with spring constant 30 N/m. At t = 0, the mass is disturbed from rest by an oscillating motor, which supplies a force of 3 cos 9.2t N to the system. After 10 seconds, the motor is switched off. We can model the forcing with the discontinuous function 3 cos 9.2t if 0 < t < 10 f(t) = %3D if t > 10. (a) Write down the initial value problem that describes this spring-mass system. (b) Solve the IVP from part (a) and express your answer as a piecewise function. Hint: First solve the IVP for 0 < t < 10, then for t > 10, and combine the two answers. Make sure the resulting function is differentiable at t = 10 (i.e. the functions and their derivatives must match up there). %3D

Advanced Engineering Mathematics
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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Problem 1 (Discontinuous Forcing). Suppose we have an undamped spring-mass system, where a 0.3 kg mass is attached to a spring with spring constant 30 N/m. At t = 0, the mass is disturbed from rest by an oscillating motor, which supplies a force of 3 cos 9.2t N to the system. After 10 seconds, the motor is switched off. We can model the forcing with the discontinuous function 3 cos 9.2t if 0 < t < 10 f(t) = %3D if t > 10. (a) Write down the initial value problem that describes this spring-mass system. (b) Solve the IVP from part (a) and express your answer as a piecewise function. Hint: First solve the IVP for 0 < t < 10, then for t > 10, and combine the two answers. Make sure the resulting function is differentiable at t = 10 (i.e. the functions and their derivatives must match up there). %3D
Transcribed Image Text:Problem 1 (Discontinuous Forcing). Suppose we have an undamped spring-mass system, where a 0.3 kg mass is attached to a spring with spring constant 30 N/m. At t = 0, the mass is disturbed from rest by an oscillating motor, which supplies a force of 3 cos 9.2t N to the system. After 10 seconds, the motor is switched off. We can model the forcing with the discontinuous function 3 cos 9.2t if 0 < t < 10 f(t) = %3D if t > 10. (a) Write down the initial value problem that describes this spring-mass system. (b) Solve the IVP from part (a) and express your answer as a piecewise function. Hint: First solve the IVP for 0 < t < 10, then for t > 10, and combine the two answers. Make sure the resulting function is differentiable at t = 10 (i.e. the functions and their derivatives must match up there). %3D
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