A 0.48-kg object is attached to one end of a spring, as in the first drawing, an
ID: 2217315 • Letter: A
Question
A 0.48-kg object is attached to one end of a spring, as in the first drawing, and the system is set into simple harmonic motion. The displacement x of the object as a function of time is shown in the second drawing. With the aid of these data, determine (a) the amplitude A of the motion, (b) the angular frequency , (c) the spring constant k, (d) the speed of the object at t = 1.0 s, and (e) the magnitude of the object's acceleration at t = 1.0 s.
***Please show all work for each part!!!
Explanation / Answer
The amplitude is A = 0.08 m The angular frequency w is 2 pi divided by the period (4 s). w = (2 pi/ 4) = pi / 2 = 1.5708 rad / s At t = 1.0 s, the elongation is maximum and the speed is thus 0 m/s The accelaration at that same time has a magnitude w^2 A = 0.1974 m/s^2 The spring constant is such that F = k A = M w^2 A k = M w^2 = 2.22 N/m
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