A 1kg glider attached to a spring with a force constant 9 N/m oscillates on a ho

Question

A 1kg glider attached to a spring with a force constant 9 N/m oscillates on a horizontal, frictionless air track. At t = 0, the glider is released from rest at x = +3.5 cm. (That is, the spring is compressed by 3.5 cm.)

(a) Find the period of its motion. (in seconds)

(b) Find the maximum values of its speed and acceleration. (in m/s and m/s^2, respectively)

(c) Find the position, velocity, and accelerations as functions of time t (in cm for position, cm/s for velocity, and cm/s^2 for acceleration)

Explanation / Answer

a ) = sqrt(k/m) = 3 N/m
   T = 1/f = 2.09 s
b)  The maximum speed of the object is
vmax = ?A = 10.5 cm/x (x = 3.5)
The maximum acceleration of the object is
amax = ?^2A = 31.5
(c) The position starts at the minimum value of x, so a cos based expression for x is in order
x = A cos(?t) = A cos(?t) (14)
v = -?A sin(?t) = -vmax sin(?t) (15)
a = -?^2A cos(?t) = -amax cos(?t) .

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