A glider on an air track oscillates with simple harmonic motion. A position sensor records displacement y (in centimeters) relative to the sensor. Because of the setup geometry, the sensor’s zero reading is not the glider’s equilibrium position; instead, when the glider is at equilibrium the sensor reads +3.0cm. A short excerpt from the displacement–time record is described below.
• At t=0.10s the sensor reading is +7.0cm, the maximum recorded during this cycle.
• The next sensor reading of +3.0cm occurs at t=0.35s.
• The minimum reading of −1.0cm occurs at t=0.60s.
• The pattern repeats with constant shape and amplitude.
Answer the following, treating the motion as ideal simple harmonic motion.
(a) Determine the numerical value of the amplitude of the glider’s oscillation about its equilibrium position. Explain how you locate both the peak and the equilibrium level in the recorded data.
(b) Using the times provided, calculate the period and frequency of the glider’s motion.
(c) Derive an expression for the displacement y(t) relative to the sensor, expressed as either a sine or cosine function that is consistent with the given data. Include all constants and phase information, and simplify your result.