A mass is attached to the end of a spring and set into oscillation on a horizont

Question

A mass is attached to the end of a spring and set into oscillation on a horizontal frictionless surface by releasing it from a stretched position. The position of the mass at any time is described by x = (5.3 cm) cos [2t/(0.67 s)]. Determine the following. (Where applicable, indicate the direction with the sign of your answer. Assume the mass is initially stretched in the positive direction.)

(a) period T of the motion

____s

(b) location of the mass at t = 3.0 s

____cm

(c) location of the mass at t = 3.0 s + T

____cm

Explanation / Answer

(a) T = 0.67 s
(b) just plug in t = 3.0 s:
x = 5.3cm * cos(2 * 3.0 / 0.67) = -5.25 cm
(c) just plug in t = (3.0 + 0.67)s = 3.67 s

x = 5.3cm * cos(2 * 3.67 / 0.67) = -5.25 cm

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