The position of a mass that is oscillating on a spring is given by x = (12.3 cm) cos[(1.26s^-1)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 position function is given by x = (12.3 cm) cos[(1.26s^-1)t]. The first derivative of the position function is given by v = dx/dt = -(12.3 cm)(1.26s^-1) sin[(1.26s^-1)t]. The second derivative of the position function is given by a = dv/dt = -(12.3 cm)(1.26s^-1)² cos[(1.26s^-1)t]. At t = 0.825 s, the acceleration of the mass is given by a = -(12.3 cm)(1.26s^-1)² cos[(1.26s^-1)(0.825 s)] = -9.89 cm/s².

The Position of a Mass That Is Oscillating on a Spring