The table below lists the measured displacement x of an object undergoing one-dimensional oscillation as a function of time t.
(Time t in s) 0.00 0.10 0.20 0.30 0.40 0.50
(Displacement x in m) +0.12 0.00 −0.12 0.00 +0.12 0.00
Assume the motion is periodic and can be represented by a single trigonometric function.
Answer the following.
(1) Determine the period of the oscillation from the data.
(2) Calculate the corresponding frequency and angular frequency.
(3) Write an explicit function x(t) that fits the data, using a cosine form with appropriate numerical parameters.
(4) Evaluate the object’s velocity and acceleration at t=0.25s.
(5) Interpret the signs of the displacement and acceleration you obtained in part (d) in terms of the object’s motion toward or away from equilibrium.