Theory of Machines

1: The equation of motion for a vibrating system with viscous damping is `(d^2 x)/(dt^2) + c/m xx (dx)/(dt) + S/m xx x =0`

if the roots of the equation are __________ then the system will be under damped.

A. equal

B. real

C. complex conjugate

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2: The ratio of velocities of the shafts connected by Hooke's joint is given by (where N and N₁ = Speed of driving and driven shafts (in r.p.m.) respectively,`theta` = Angle through which the arms of the cross turn, and `alpha` = Angle of inclination between the two shafts)

A. `N/N_1 = (1 - cos ^2 theta sin ^2 alpha)/(cos alpha)`

B. `N/N_1 = (1 - cos ^2 alpha sin ^2 theta)/(cos alpha)`

C. `N/N_1 = (cos alpha )/(1 - cos ^2 theta sin ^2 alpha)`

D. `N/N_1 = (cos alpha )/(1 - cos ^2 alpha sin ^2 theta)`

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3: In a flat collar pivot bearing, the moment due to friction is proportional to

A. `((r_1^2 - r_2^2)/(r_1 - r_2))`

B. `((r_1^2 - r_2^2)/(r_1 + r_2))`

C. `((r_1^3 - r_2^3)/(r_1^2 - r_2^2))`

D. `((r_1^3 - r_2^3)/(r_1- r_2))`

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4: One end of a helical spring is fixed while the other end carries the load W which moves with simple harmonic motion. The frequency of motion is given by (where `delta` = Deflection of the spring)

A. `2n sqrt(g/delta)`

B. `(1)/(2n) sqrt(g/delta)`

C. `2n sqrt(delta/g)`

D. `(1)/(2n) sqrt(delta/g)`

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A. `(tan (alpha + phi))/(tan alpha)`

B. `(tan alpha)/(tan (alpha + phi))`

C. `(tan (alpha - phi))/(tan alpha)`

D. `(tan alpha)/(tan (alpha - phi))`

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