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QUESTION 2 Vibration absorber (also called tuned mass damper) is used to reduce* the vibration at the natural frequency of the original system. Consider a M-K system shown below. Original System x(t) Modified System x₁(1) X2(t) K M F(t) K M m F(t) absorber K This system has a natural frequency at rad. The absorber mass and the spring are attached to the original system as shown in the figure, and the values are selected so that (1) the amplitude of the original mass, M, at M the original natural frequency is zero, and (2) the new natural frequencies are moved away from the original natural frequency. The selection of absorber mass and stiffness, m and k, is easy. They have the same ratio as the ratio of the original system. That is, M/m = KIK. Find the transfer functions X1(s)/F(s) and X2(s)/F(s) before you can answer questions. * I said "reduce," but for undamped system, it can be completely eliminated. What is the response amplitude (particular solution only) of the second mass if F(t) = 185 sin(wt)? Use scientific notation with 3 signifincant figures. Omit units. K Let M = 4 kg, K = 150 N/m, M/m = K/k7, and w = 0.3. M

QUESTION 2 Vibration absorber (also called tuned mass damper) is used to reduce* the vibration at the natural frequency of the original system. Consider a M-K system shown below. Original System x(t) Modified System x₁(1) X2(t) K M F(t) K M m F(t) absorber K This system has a natural frequency at rad. The absorber mass and the spring are attached to the original system as shown in the figure, and the values are selected so that (1) the amplitude of the original mass, M, at M the original natural frequency is zero, and (2) the new natural frequencies are moved away from the original natural frequency. The selection of absorber mass and stiffness, m and k, is easy. They have the same ratio as the ratio of the original system. That is, M/m = KIK. Find the transfer functions X1(s)/F(s) and X2(s)/F(s) before you can answer questions. * I said "reduce," but for undamped system, it can be completely eliminated. What is the response amplitude (particular solution only) of the second mass if F(t) = 185 sin(wt)? Use scientific notation with 3 signifincant figures. Omit units. K Let M = 4 kg, K = 150 N/m, M/m = K/k7, and w = 0.3. M

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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QUESTION 2 Vibration absorber (also called tuned mass damper) is used to reduce* the vibration at the natural frequency of the original system. Consider a M-K system shown below. Original System x(t) Modified System x₁(1) X2(t) K M F(t) K M m F(t) absorber K This system has a natural frequency at rad. The absorber mass and the spring are attached to the original system as shown in the figure, and the values are selected so that (1) the amplitude of the original mass, M, at M the original natural frequency is zero, and (2) the new natural frequencies are moved away from the original natural frequency. The selection of absorber mass and stiffness, m and k, is easy. They have the same ratio as the ratio of the original system. That is, M/m = KIK. Find the transfer functions X1(s)/F(s) and X2(s)/F(s) before you can answer questions. * I said "reduce," but for undamped system, it can be completely eliminated. What is the response amplitude (particular solution only) of the second mass if F(t) = 185 sin(wt)? Use scientific notation with 3 signifincant figures. Omit units. K Let M = 4 kg, K = 150 N/m, M/m = K/k7, and w = 0.3. M
Transcribed Image Text:QUESTION 2 Vibration absorber (also called tuned mass damper) is used to reduce* the vibration at the natural frequency of the original system. Consider a M-K system shown below. Original System x(t) Modified System x₁(1) X2(t) K M F(t) K M m F(t) absorber K This system has a natural frequency at rad. The absorber mass and the spring are attached to the original system as shown in the figure, and the values are selected so that (1) the amplitude of the original mass, M, at M the original natural frequency is zero, and (2) the new natural frequencies are moved away from the original natural frequency. The selection of absorber mass and stiffness, m and k, is easy. They have the same ratio as the ratio of the original system. That is, M/m = KIK. Find the transfer functions X1(s)/F(s) and X2(s)/F(s) before you can answer questions. * I said "reduce," but for undamped system, it can be completely eliminated. What is the response amplitude (particular solution only) of the second mass if F(t) = 185 sin(wt)? Use scientific notation with 3 signifincant figures. Omit units. K Let M = 4 kg, K = 150 N/m, M/m = K/k7, and w = 0.3. M
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