Applied Mechanics and Graphic Statics
The ratio of the ranges on the inclined plane with motion upward and with motion downward for a given velocity, angle of projection will be

sin (α + β)/sin (α - β)
tan (α - β)/tan (α + β)
cos (α - β)/cos (α + β)
sin (α - β)/sin (α + β)

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Applied Mechanics and Graphic Statics
Lami's theorem states that

Three coplanar forces acting at a point will be in equilibrium, if each force is proportional to the sine of the angle between the other two
Three coplanar forces acting at a point will be in equilibrium if each force is inversely proportional to the sine of the angle between the other two
Three forces acting at a point are always in equilibrium
If three forces acting on a point can be represented in magnitude and direction by the sides of a triangle, the point will be in the state of equilibrium

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Applied Mechanics and Graphic Statics
One end of an elastic string of natural length ‘l’ and modulus ‘X’ is kept fixed while to the other end is attached a particle of mass m which is hanging freely under gravity. The particle is pulled down vertically through a distance ‘x’, held at rest and then released.The motion is

A rectilinear motion with constant speed
A simple harmonic motion
A damped oscillatory motion
None of these

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