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A 1.00-kg glider attached to a spring with a force constant 25.0 N/m oscillates

ID: 1300909 • Letter: A

Question

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 = -3.50 cm (that is, the spring is compressed by 3.50 cm).

(a) Find the period of the glider's motion.
s

(b) Find the maximum values of its speed and acceleration.


(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.)

speed m/s acceleration m/s2

Explanation / Answer

(a)
Period = 2pi sqrt(1.00 / 25.0)
= 1.26 sec.

(b)
Max. speed = 3.50 sqrt(5)
= 7.83 cm/sec.

Max. acceleration
= 5 * 3.50
= 17.50 cm/sec^2.

(c)
x = - 3.50 cos[ t sqrt(5) ] cm.
x' = 3.50 sqrt(5) sin[ t sqrt(5) ] cm/sec.
x'' = 17.50 cos[ t sqrt(5) ] cm/sec^2.