A block attached to an ideal horizontal spring oscillates along a friction-free track. A sensor records the block’s displacement x from the track’s center point as a function of time. The sensor output, converted to a graph, can be described as follows:
• The vertical axis is displacement in centimeters, with tick marks every 1cm.
• The horizontal axis is time in seconds, with tick marks every 0.25s.
• The graph passes through its maximum value of +4cm at t=0s, its next zero crossing occurs at t=0.25s, and its next minimum value of −4cm occurs at t=0.50s.
• The pattern then repeats with no change in shape or size for the duration of the record.
Using only the verbal description above, answer the following questions about the motion of the block.
(a) Describe the feature(s) of the graph that allow you to determine the amplitude of the oscillation, and state the amplitude with appropriate units.
(b) Explain how the period of the motion can be inferred from the given times and determine its numerical value.
(c) Using your answer to part (b), determine the frequency of the oscillation and explain the mathematical relationship between period and frequency.
(d) At t=0s the displacement is a positive maximum. Discuss whether the cosine or sine mathematical form more naturally represents x(t) for this system, and justify your choice in terms of phase.