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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

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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Differential Equation 

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
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
Expert Solution
Solution a:

The undamped spring-mass system is given by my''+ky=ft.

Here, m=0.3 and k=30

0.3y''+30y=3cos9.2tif 0≤t<100if t≥10, y0=0, y'0=0

For 0≤t<10, the non homogeneous equation is 0.3y''+30y=3cos9.2t⇒y''+100y=10cos9.2t.

Solve the homogeneous equation y''+100y=0.

The characteristic equation is m2+100=0⇒m=±10i.

Thus, the homogeneous solution is yh=c1cos10t+c2sin10t

 

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