A 1.00 kg glider attached to a spring with a force constant9.0 N/m oscillates on

Question

A 1.00 kg glider attached to a spring with a force constant9.0 N/m oscillates on a horizontal,frictionless air track. At t = 0, the glider is releasedfrom rest at x = +3.00 cm. (That is,the spring is compressed by 3.00 cm.) (a) Find the period of its motion.
1 s
(b) Find the maximum values of its speed and acceleration.
2 m/s
3 m/s2
(c) Find the position, velocity, and acceleration as functions oftime (t).
4cm (position)
5cm/s (velocity)
6cm/s2 (acceleration)
(a) Find the period of its motion.
1 s
(b) Find the maximum values of its speed and acceleration.
2 m/s
3 m/s2
(c) Find the position, velocity, and acceleration as functions oftime (t).
4cm (position)
5cm/s (velocity)
6cm/s2 (acceleration)

Explanation / Answer

m = 1.00 kg, k = 9.0 N/m, t = 0, x = 3.00 cm, so amplitude A = 3.00 cm a) = (k/m) = 3.0 rad/s period t = 2/ = 2.09 s b) maximum speed = A = 9.0 cm/s = 0.090 m/s maximum acceleration = 2A = 27 cm/s = 0.27 m/s c) x(t) = Acos(t) = 3.00cos(3t) v(t) = -9.0sin(3t) a(t) = -27cos(3t)

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