#### 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

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)

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))

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)

5
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))