Theory of Machines


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


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)`


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))`

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)`

Efficiency of a screw jack is given by

A. `(tan (alpha + phi))/(tan alpha)`
B. `(tan alpha)/(tan (alpha + phi))`
C. `(tan (alpha - phi))/(tan alpha)`
D. `(tan alpha)/(tan (alpha - phi))`