The position of a mass that is oscillating on a spring is given by x = (12.3 cm) cos[(1.26 s²)t]. What is the acceleration of the mass when t = 0.825 s? A) 9.89 cm/s² B) -9.89 cm/s² C) 10.6 cm/s² D) -10.6 cm/s² E) 0 cm/s²

Question

Quizplus · Accepted Answer

The acceleration of the mass is given by the second derivative of the position function with respect to time. The second derivative of cos(t) is -cos(t), so the acceleration of the mass is given by:a = -Aω^2cos(ωt)where A is the amplitude of the oscillation, ω is the angular frequency, and t is the time.At t = 0.825 s, the acceleration of the mass is:a = -(12.3 cm)(1.26 s^-2)^2cos[(1.26 s^-2)(0.825 s)] = -9.89 cm/s^2Therefore, the correct answer is B.

The Position of a Mass That Is Oscillating on a Spring