In simple harmonic motion (SHM), the general equations for position, velocity, and acceleration are:
x(t) = A cos(ωt + φ)
|= - A ω sin(ωt + φ)|
|= - A ω2 cos(ωt + φ)|
The phase angle φ is determined by the initial position and initial velocity.
The constant multiplying the sine or cosine represents the maximum displacement. Thus:
xmax = A vmax = Aω amax = Aω2
Graphing the position, velocity, and acceleration reveal general features of SHM:
The first set of graphs is for ω = 1 rad/s. The second set is for ω = 0.6 rad/s. This change of ω is accomplished either by decreasing the spring constant or by increasing the mass. Which change was made in this case?