2.. 3/6 points ! Previous Answers SerPSET9 15P018 My NotesAsk Your Teacher A 1.0

Question

2.. 3/6 points ! Previous Answers SerPSET9 15P018 My NotesAsk Your Teacher A 1.00-kg glider attached to a spring with a force constant 25.0 N/m oscillates on a frictionless, horizontal air track. At t = 0, the glider is released from rest at x =-3.10 cm (that is, the spring is compressed by 3.10 cm). (a) Find the period of the glider's motion. 1.256 (b) Find the maximum values of its speed and acceleration. speed 0.155 acceleration 0.775 m/s m/s2 (c) Find the position, velocity, and acceleration as functions of time. (Where position is in m, velocity is in m/s, acceleration is in m/s2, and t is in s. Use the following as necessary: t.) x(t) = 3.1 cos(5t) X v(t) =|-0.155 sin(5t) X a(t) =I-0.775 cos(51) | x

Explanation / Answer

Since the glider is at maximum amplitude at t = 0, model with the cos function:
x(t) = -Acos(t) = -3.10cm * cos(5t) for t in seconds
v(t) = dx/dt = Asin(t) = 15.5cm/s * sin(5t)
a(t) = dv/dt = A²cos(t) = 77.5cm/s² * cos(5t)

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