Question

It is already shown that the influence of the damper coefficient on the natural frequencies of the modern suspension systems is little. Ignoring the effect of damper and using Figure Q4-1, extract parametric equations for the natural frequencies of a modern suspension system. Hint: You need to write down the equations of motion for two masses, take the Laplace transform of the equations and replace $s = j\omega$. The resulting equations will be in the form of $A\begin{bmatrix} z_{us} \\ z_s \end{bmatrix}^T = 0$ and $A = \begin{bmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{bmatrix}$, which is valid for all $\begin{bmatrix} z_{us} & z_s \end{bmatrix}^T$ if $det(A) = a_{11}a_{22} - a_{12}a_{21} = 0$. k_s = k k_t = 15k $m_s = 5m$ $m_s = m$ Figure Q4-1 Simplified quarter-car model

          It is already shown that the influence of the damper coefficient on the
natural frequencies of the modern suspension systems is little. Ignoring
the effect of damper and using Figure Q4-1, extract parametric equations
for the natural frequencies of a modern suspension system.
Hint: You need to write down the equations of motion for two masses, take the
Laplace transform of the equations and replace $s = j\omega$. The resulting equations
will be in the form of $A\begin{bmatrix} z_{us} \\ z_s \end{bmatrix}^T = 0$ and $A = \begin{bmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{bmatrix}$, which is valid for all
$\begin{bmatrix} z_{us} & z_s \end{bmatrix}^T$ if $det(A) = a_{11}a_{22} - a_{12}a_{21} = 0$.
k_s = k
k_t = 15k
$m_s = 5m$
$m_s = m$
Figure Q4-1 Simplified quarter-car model

It is already shown that the influence of the damper coefficient on the
natural frequencies of the modern suspension systems is little. Ignoring
the effect of damper and using Figure Q4-1, extract parametric equations
for the natural frequencies of a modern suspension system.
Hint: You need to write down the equations of motion for two masses, take the
Laplace transform of the equations and replace s = jω. The resulting equations
will be in the form of A
< b m a t r i x >
^T = 0 and A =
< b m a t r i x >, which is valid for all
< b m a t r i x >
^T if det(A) = a11a22 - a12a21 = 0.
ks = k
kt = 15k
ms = 5m
ms = m
Figure Q4-1 Simplified quarter-car model

Added by Ricky P.

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