A laboratory mass–spring system is monitored with a velocity probe that outputs the instantaneous velocity v of the mass as a function of time. The probe’s velocity–time graph is summarized verbally below.
• The horizontal axis is time in seconds; the vertical axis is velocity in meters per second.
• The graph first reaches a positive peak of +0.30ms−1 at t=0.20s.
• Immediately afterward, the graph crosses zero at t=0.35s.
• A negative peak of −0.30ms−1 occurs at t=0.50s.
• The pattern repeats with the same shape and size.
Assume the motion is ideal simple harmonic motion.
(a) Use the features of the velocity graph to determine the period of the underlying oscillation of the mass.
(b) From the period, calculate the angular frequency ω of the motion.
(c) Determine the numerical value of the amplitude A of the mass’s displacement from equilibrium. Clearly outline how information from a velocity–time graph can be used to obtain A.
(d) Construct a complete equation for the displacement x(t) as a function of time that is consistent with the velocity graph and your calculated parameters. Explicitly state any phase angle included in your expression.