The natural frequency of free transverse vibrations due to a point load acting over a simply supported shaft is equal to (where $$\delta $$ = Static deflection of a simply supported shaft due to the point load)

The natural frequency of free transverse vibrations due to uniformly distributed load acting over a simply supported shaft is (where $$\delta {\text{S}}$$ = Static deflection of simply supported shaft due to uniformly distributed load)

A

$$\frac{{0.4985}}{{\sqrt {\delta {\text{S}}} }}$$

B

$$\frac{{0.5615}}{{\sqrt {\delta {\text{S}}} }}$$

C

$$\frac{{0.571}}{{\sqrt {\delta {\text{S}}} }}$$

D

$$\frac{{0.6253}}{{\sqrt {\delta {\text{S}}} }}$$

The natural frequency of free longitudinal vibrations is equal to (where m = Mass of the body, s = Stiffness of the body and $$\delta $$ = Static deflection of the body)

A

$$\frac{1}{{2\pi }} \times \sqrt {\frac{{\text{s}}}{{\text{m}}}} $$

B

$$\frac{1}{{2\pi }} \times \sqrt {\frac{{\text{g}}}{\delta }} $$

C

$$\frac{{0.4985}}{{\sqrt \delta }}$$

D

Any one of these

The natural frequency of free torsional vibrations of a shaft is equal to (where q = Torsional stiffness of the shaft and $$I$$ = Mass moment of inertia of the disc attached at the end of a shaft)

A

$$2\pi \sqrt {\frac{{\text{q}}}{I}} $$

B

$$2\pi \sqrt {{\text{q}}I} $$

C

$$\frac{1}{{2\pi }}\sqrt {\frac{{\text{q}}}{I}} $$

D

$$\frac{1}{{2\pi }}$$

The frequency of damped vibrations with viscous damping is ________ the frequency of undamped vibrations.

A

More than

B

Less than

C

Same as

D

None of these

A simply supported uniform rectangular bar breadth b, depth d and length L carries an isolated load W at its mid-span. The same bar experiences an extension e under same tensile load. The ratio of the maximum deflection to the elongation, is

A

$$\frac{{\text{L}}}{{\text{d}}}$$

B

$$\frac{{\text{L}}}{{2{\text{d}}}}$$

C

$${\left( {\frac{{\text{L}}}{{2{\text{d}}}}} \right)^2}$$

D

$${\left( {\frac{{\text{L}}}{{3{\text{d}}}}} \right)^2}$$

In a system subjected to damped forced vibrations, the ratio of maximum displacement to the static deflection is known as

A

Critical damping ratio

B

Damping factor

C

Logarithmic decrement

D

Magnification factor

A simply supported beam 'A' of length l, breadth b, and depth d carries a central point load W. Another beam 'B' has the same length and depth but its breadth is doubled. The deflection of beam 'B' will be __________ as compared to beam 'A'.

A

One-fourth

B

One-half

C

Double

D

Four times

For a simply supported beam of length 'L', when a concentrated load W is applied in the center of the beam, the maximum deflection is

A

$$\frac{{5{\text{W}}{{\text{L}}^3}}}{{384{\text{EI}}}}$$

B

$$\frac{{{\text{W}}{{\text{L}}^3}}}{{384{\text{EI}}}}$$

C

$$\frac{{{\text{W}}{{\text{L}}^3}}}{{348{\text{EI}}}}$$

D

$$\frac{{{\text{W}}{{\text{L}}^3}}}{{48{\text{EI}}}}$$

The critical speed of a shaft in revolution per second is __________ as that of natural frequency of transverse vibration.

A

Same

B

Different

C

Unpredictable

D

None of these

The product of the tangential force acting on the shaft and its distance from the axis of the shaft (i.e. radius of shaft) is known as

A

Bending moment

B

Twisting moment

C

Torsional rigidity

D

Flexural rigidity

The natural frequency of free transverse vibrations due to a point load acting over a simply supported shaft is equal to (where $$\delta $$ = Static deflection of a simply supported shaft due to the point load)

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