An accelerometer fixed to the platform of a low-friction cart records the cart’s acceleration a along a straight line as a function of time. A segment of the acceleration–time record, covering slightly more than one full cycle, is verbally summarized below. Random laboratory noise causes small fluctuations of no more than ±5% of the peak values.
• The greatest positive acceleration, +0.40ms−2, occurs at t=0.12s.
• Zero acceleration readings occur at t=0.00s and again at t=0.24s.
• The greatest negative acceleration, −0.40ms−2, occurs at t=0.36s.
• Beyond t=0.48s the pattern repeats.
Treat the motion as ideal simple harmonic motion and disregard the small random fluctuations when determining numerical values.
(a) Estimate the period of the cart’s motion using the zero crossings of the acceleration graph. Justify the use of zero crossings instead of extrema for period determination in this context.
(b) Using your period from part (a), calculate the corresponding angular frequency ω.
(c) Derive the amplitude of the cart’s displacement oscillation. Provide a step-by-step explanation beginning with the information available from the acceleration graph.
(d) Sketch a qualitative graph of velocity versus time for one full cycle, labeling key points (maxima, minima, and zeros) with their approximate times. Explain the reasoning that guided your sketch.