Question

Problem 5: modeling mechanical system Figure 2 shows the simplified diagram of the printwheel control system of a word processor. The printwheel is controlled by a DC motor through belts and pulleys. Assume that the belts are rigid. The following parameters and variables are defined: $ au_m(t)$ is the motor torque; $ heta(t)$, the motor angle; $y(t)$, the linear displacement of the printwheel; $J_m$, the motor inertia; $B_m$ the motor viscous-friction coefficient; $r$, the pulley radius; and $M$, the mass of the printwheel. au_m Motor $J_m$ $B_m$ Printwheel M r y(t) Pulley Figure 2: Trailer-towing system (a) Write the differential equation of the system (b) Find the transfer function $frac{Y(s)}{ au_m(s)}$ where $ au_m(s)$ and $Y(s)$ are the Laplace transform of $ au_m(t)$ and $y(t)$, respectively.

          Problem 5: modeling mechanical system
Figure 2 shows the simplified diagram of the printwheel control system of a word processor. The printwheel is
controlled by a DC motor through belts and pulleys. Assume that the belts are rigid. The following parameters
and variables are defined: $	au_m(t)$ is the motor torque; $	heta(t)$, the motor angle; $y(t)$, the linear displacement of the
printwheel; $J_m$, the motor inertia; $B_m$ the motor viscous-friction coefficient; $r$, the pulley radius; and $M$, the
mass of the printwheel.
	au_m
Motor
$J_m$
$B_m$
Printwheel
M
r
y(t)
Pulley
Figure 2: Trailer-towing system
(a) Write the differential equation of the system
(b) Find the transfer function $frac{Y(s)}{	au_m(s)}$ where $	au_m(s)$ and $Y(s)$ are the Laplace transform of $	au_m(t)$ and $y(t)$, respectively.

$Problem 5: modeling mechanical system Figure 2 shows the simplified diagram of the printwheel control system of a word processor. The printwheel is controlled by a DC motor through belts and pulleys. Assume that the belts are rigid. The following parameters and variables are defined: aum(t) is the motor torque; heta(t), the motor angle; y(t), the linear displacement of the printwheel; Jm, the motor inertia; Bm the motor viscous-friction coefficient; r, the pulley radius; and M, the mass of the printwheel. aum Motor Jm Bm Printwheel M r y(t) Pulley Figure 2: Trailer-towing system (a) Write the differential equation of the system (b) Find the transfer function fracY(s) aum(s) where aum(s) and Y(s) are the Laplace transform of aum(t) and y(t), respectively.$

Added by Sally V.

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