If $$\frac{\omega }{{\omega {\text{n}}}} = 2,$$ where co is the frequency of excitation and $${\omega {\text{n}}}$$ is the natural frequency of vibrations, then the transmissibility of vibration will the

Which of the following are the basic differences between vibration signature and noise signature? 1. Vibration signature is essentially in the frequency range zero to 100 cps whereas noise signature is in the range 20 cps to 3000 cps. 2. Vibration signature has well-defined peaks whereas the noise signal is smeared. 3. The intensities of noise signatures arc much less than that of vibration signatures. 4. Detection of vibration signature calls for a microphone whereas that of noise can do with a pickup. Select the correct answer using the code given below.

A

1 and 4

B

2 and 3

C

1 and 2

D

3 and 4

Statement: Resonance is a special case of forced vibration in which the nature and frequency of vibration of the body are the same as the impressed frequency and the amplitude of forced vibration, is maximum. Reason: The amplitude of forced vibrations of a body increases with an increase in the frequency of the externally impressed periodic force.

A

Both statement and reason are true and the reason is the correct explanation of the statement

B

Both statement and reason are true but the reason is not the correct explanation of the statement

C

Statement is true, but the reason is false

D

Statement and reason are false

Two monochromatic waves having frequencies $$\omega $$ and $$\omega + \Delta \omega \left( {\Delta \omega \ll \omega } \right)$$ and corresponding wavelengths $$\lambda $$ and $$\lambda - \Delta \lambda \left( {\Delta \lambda \ll \lambda } \right)$$ of same polarization, travelling along X-axis are superimposed on each other. The phase velocity and group velocity of the resultant wave are respectively given by

A

$$\frac{{\omega \lambda }}{{2\pi }},\,\frac{{\Delta \omega {\lambda ^2}}}{{2\pi \Delta \lambda }}$$

B

$$\omega \lambda ,\,\frac{{\Delta \omega {\lambda ^2}}}{{\Delta \lambda }}$$

C

$$\frac{{\omega \Delta \lambda }}{{2\pi }},\,\frac{{\Delta \omega \Delta \lambda }}{{2\pi }}$$

D

$$\omega \Delta \lambda ,\,\omega \Delta \lambda $$

In vibration isolation system, the transmissibility will be equal to unity, for all values of damping factor, if $$\frac{\omega }{{\omega {\text{n}}}}$$ is

A

Equal to 1

B

Equal to 2

C

Less than 2

D

Greater than 2

If 30Ω6 = -5, 80Ω2 = -40 and 20Ω4 = -5, then find the value of 70Ω2 = ?

A

10

B

-35

C

15

D

-20

If 7Ω6 = 84, 8Ω7 = 112 and 8Ω4 = 64, then find the value of 3Ω4 = ?

A

24 \

B

12 \

C

4 \

D

20

If 7Ω6 = 84, 8Ω7 = 112 and 8Ω4 = 64, then find the value of 3Ω4 = ?

A

24 \

B

12

C

4 \

D

20

For a function g(t), it is given that
$$\int\limits_{ - \infty }^{ + \infty } {g\left( t \right){e^{ - j\omega t}}dt = \omega {e^{ - 2{\omega ^2}}}} $$ for any real value $$\omega $$ . If $$y\left( t \right) = \int\limits_{ - \infty }^t {g\left( \tau \right)} d\tau ,\,{\rm{then}}\,\int\limits_{ - \infty }^{ + \infty } {y\left( t \right)} dt$$ is. . . . . . . .

A

0

B

-j

C

$$ - {j \over 2}$$

D

$${j \over 2}$$

The raised cosine pulse p(t) is used for zero ISI in digital communications. The expression for p(t) with unity roll-off factor is given by $$p\left( t \right) = \frac{{\sin 4\pi \omega t}}{{4\pi \omega t\left( {1 - 16{\omega ^2}{t^2}} \right)}}.$$ The value of p(t) at $$t = \frac{1}{{4\omega }}$$ is

A

-0.5

B

0

C

0.5

D

∞

The Fourier transform of a signal
h(t) is $$H\left( {j\omega } \right) = {{\left( {2\cos \omega } \right)\left( {\sin \omega } \right)} \over \omega }$$
The value of h(0) is

A

$${1 \over 4}$$

B

$${1 \over 2}$$

C

1

D

2

If $$\frac{\omega }{{\omega {\text{n}}}} = 2,$$ where co is the frequency of excitation and $${\omega {\text{n}}}$$ is the natural frequency of vibrations, then the transmissibility of vibration will the

Related Questions