$2\mathrm{.}1$ Figure $2\mathrm{.}42$ shows the block diagram of a closed$-$loop servo accelerometer. The

accelerometer functions as follows: a pendulous mass reacts to an acceleration input and begins

to move. A position sensor detects this minute motion and develops an output signal. This signal

is demodulated, amplified, and applied as negative feedback to an electrical torque generator

$($torquer$)$ coupled to the mass. The torquer develops a torque proportional to the current applied

to it$.$ The magnitude and direction of this torque just balance out the torque attempting to move

the pendulous mass as a result of the acceleration input, preventing further movement of the

mass.

Since both torques are equal and the torque generator output is proportional to its input current,

the input current is$,$ therefore, proportional to the torque attempting to move the pendulous mass.

In fact, this torque is proportional to the product of moment of inertia and acceleration.

Therefore, the torque generator current is proportional to applied acceleration. If this current is

passed through a stable resistor, the voltage developed is proportional to applied acceleration:

Draw a reliability graph of the feedback system.

Assuming that the probability that a component functioning properly is $0\mathrm{.}9,$ what is the total

system reliability when all components have the same probability of success?

FIGURE $2\mathrm{.}42$ A block diagram for Problem $2\mathrm{.}1.$