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

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Applied Mechanics and Graphic Statics
One end of an elastic string of natural length / 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 simple harmonic motion
a damped oscillatory motion
a rectilinear motion with constant speed
None of these

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