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enyata [817]
3 years ago
7

A second order measuring system has a known natural frequency of 2000 Hz and damping ratio of 0.8. Would it be satisfactory to u

se it to measure a signal expected to have frequency content at up to 500 Hz? Demonstrate your answer by finding the expected dynamic error and phase shift at 500 Hz.

Physics
1 answer:
Anna007 [38]3 years ago
7 0

Answer:

The  expected dynamic error is  0.019

The phase shift is -23.10°C

Explanation:

The explanation is shown on the first uploaded image

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The equation Bold r (t )equals(8 t plus 9 )Bold i plus (2 t squared minus 8 )Bold j plus (6 t )Bold k is the position of a parti
KATRIN_1 [288]

Explanation:

It is given that, the position of a particle as as function of time t is given by :

r(t)=(8t+9)i+(2t^2-8)j+6tk

Let v is the velocity of the particle. Velocity of an object is given by :

v=\dfrac{dr(t)}{dt}

v=\dfrac{d[(8t+9)i+(2t^2-8)j+6tk]}{dt}

v=(8i+4tj+6k)\ m/s

So, the above equation is the velocity vector.

Let a is the acceleration of the particle. Acceleration of an object is given by :

a=\dfrac{dv(t)}{dt}

a=\dfrac{d[8i+4tj+6k]}{dt}

a=(4j)\ m/s^2

At t = 0, v=(8i+0+6k)\ m/s

v(t)=\sqrt{8^2+6^2} =10\ m/s

Hence, this is the required solution.

7 0
3 years ago
A motorboat traveling with a current can go 160 km in 4 hours. against the current it takes 5 hours to go the same distance. Fin
MatroZZZ [7]
<h2>Speed of motorboat is 36 km/hr and speed of current is 4 km/hr.</h2>

Explanation:

Let speed of motor boat be m and speed of current be c.

A motorboat traveling with a current can go 160 km in 4 hours.

   Distance = 160 km

   Time = 4 hours

    Speed = m + c

   We have

            Distance = Speed x Time

            160 = (m+c) x 4

            m + c = 40     --------------------- eqn 1

Against the current it takes 5 hours to go the same distance.

   Distance = 160 km

   Time = 5 hours

    Speed = m - c

   We have

            Distance = Speed x Time

            160 = (m-c) x 5

            m - c = 32     --------------------- eqn 2

eqn 1 + eqn 2

           2m = 40 + 32

             m = 36 km/hr

Substituting in eqn 1

               36 + c = 40

                      c = 4 km/hr

Speed of motorboat is 36 km/hr and speed of current is 4 km/hr.

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3 years ago
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Which phrase best describes a gravitational force?
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