4.12. Figure 4.20 plots the magnitude of the steady-state oscillation of a mass sub- jected to a vibrating base. For some applications, such as an automotive suspension, the magnitude of the response is not the critical factor, but rather the net force to which the mass is subjected. 1. Determine an expression for the force to which the mass illustrated in Figure 4.18 is subjected. 2. Manipulate the expression for the force so that it is in the form of f=-khMycos(cot + o). Explain the interpretation of the term Mf, which is called the force transmissi- bility. Plot My as a function of /0,, for various damping ratios to make a plot similar to Figure 4.20. displacement transmissibilty C 2 1 0.5 0 0 1 2 3 3 C=0.2 C=0.4 =0.6 C=0.8 C=1.0 Fig. 4.20 Displacement transmissibility as a function of frequency ratio and damping ratio.
4.12. Figure 4.20 plots the magnitude of the steady-state oscillation of a mass sub- jected to a vibrating base. For some applications, such as an automotive suspension, the magnitude of the response is not the critical factor, but rather the net force to which the mass is subjected. 1. Determine an expression for the force to which the mass illustrated in Figure 4.18 is subjected. 2. Manipulate the expression for the force so that it is in the form of f=-khMycos(cot + o). Explain the interpretation of the term Mf, which is called the force transmissi- bility. Plot My as a function of /0,, for various damping ratios to make a plot similar to Figure 4.20. displacement transmissibilty C 2 1 0.5 0 0 1 2 3 3 C=0.2 C=0.4 =0.6 C=0.8 C=1.0 Fig. 4.20 Displacement transmissibility as a function of frequency ratio and damping ratio.
Elements Of Electromagnetics
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![**4.12**. Figure 4.20 plots the magnitude of the steady-state oscillation of a mass subjected to a vibrating base. For some applications, such as an automotive suspension, the magnitude of the response is not the critical factor, but rather the net force to which the mass is subjected.
1. Determine an expression for the force to which the mass illustrated in Figure 4.18 is subjected.
2. Manipulate the expression for the force so that it is in the form of
\[
f = -khM_f \cos(\omega t + \phi).
\]
Explain the interpretation of the term \(M_f\), which is called the **force transmissibility**. Plot \(M_f\) as a function of \(\omega / \omega_n\) for various damping ratios to make a plot similar to Figure 4.20.
---
**Figure Explanation:** Figure 4.20 shows a graph of displacement transmissibility versus the frequency ratio (\(\omega / \omega_n\)). The graph includes several curves representing different damping ratios (\(\zeta\)):
- Curve for \(\zeta = 0.2\)
- Curve for \(\zeta = 0.4\)
- Curve for \(\zeta = 0.6\)
- Curve for \(\zeta = 0.8\)
- Curve for \(\zeta = 1.0\)
The vertical axis represents displacement transmissibility, ranging from 0 to 2.5. The horizontal axis represents the frequency ratio, ranging from 0 to 5. Each curve shows how displacement transmissibility changes at different frequencies and damping ratios.
**Fig. 4.20** Displacement transmissibility as a function of frequency ratio and damping ratio.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6a0a5ea8-ad8e-4285-a3d6-a06220c808d0%2F46d73f56-66ee-45c4-a28f-cb14fb75bf3e%2Fi84k8pd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**4.12**. Figure 4.20 plots the magnitude of the steady-state oscillation of a mass subjected to a vibrating base. For some applications, such as an automotive suspension, the magnitude of the response is not the critical factor, but rather the net force to which the mass is subjected.
1. Determine an expression for the force to which the mass illustrated in Figure 4.18 is subjected.
2. Manipulate the expression for the force so that it is in the form of
\[
f = -khM_f \cos(\omega t + \phi).
\]
Explain the interpretation of the term \(M_f\), which is called the **force transmissibility**. Plot \(M_f\) as a function of \(\omega / \omega_n\) for various damping ratios to make a plot similar to Figure 4.20.
---
**Figure Explanation:** Figure 4.20 shows a graph of displacement transmissibility versus the frequency ratio (\(\omega / \omega_n\)). The graph includes several curves representing different damping ratios (\(\zeta\)):
- Curve for \(\zeta = 0.2\)
- Curve for \(\zeta = 0.4\)
- Curve for \(\zeta = 0.6\)
- Curve for \(\zeta = 0.8\)
- Curve for \(\zeta = 1.0\)
The vertical axis represents displacement transmissibility, ranging from 0 to 2.5. The horizontal axis represents the frequency ratio, ranging from 0 to 5. Each curve shows how displacement transmissibility changes at different frequencies and damping ratios.
**Fig. 4.20** Displacement transmissibility as a function of frequency ratio and damping ratio.
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