Characteristic equations of basic curves

Curves	Displacement,y	Velocity, v	Acceleration,a
Straight Line	hθ/β	ωh/β	0
Circular Arc	H-[H2-(Rpθ)2]1/2	ωRp2θ/[H2-(Rpθ)2]1/2	(ωRpH)2/[H2- (Rpθ)2]3/2
SHM	h/2(1-cos πθ/β)	hπω/2β sinπθ/β	h/2(πω/β)2 cosπθ/β
Double harmonic	h/2[(1-cosπθ/β)-1/4(1-cos2πθ/β)]	h/2 πω/β(sin πθ/β- 1/2sin2 πθ/β)	h/2 (πω/β)2(cos πθ/β-cos2πθ/β).
Cycloidal	h/π(πθ/β-1/2sin2πθ/β).	hω/β(1-cos2πθ/β)	2hπω2/β2sin2πθ/β
Parabolic θ/β<=0.5	2h(θ/β)2	4hθω/β2	4h(ω/β)2
θ/β>=0.5	h[1-2(1- θ/β)2]	4hω/β(1- θ/β).	-4h(ω/β)2
Cubic no.1 θ/β<=0.5	4h (θ/β)3	12hω/β(θ/β)2	24hω2/β2(θ/β)
θ/β>=0.5	h[1-4(1-θ/β)3]	12hω/β((1-θ/β)2	-24hω2/β2(1-θ/β)
Cubic no.2	hθ2/β2(3-2θ/β)	6hωθ/β2(1-θ/β)	6hω2/β2(1-2θ/β)