A 1.00-kg glider attached to a spring with a force constant 16.0 N/m oscillates

Question

A 1.00-kg glider attached to a spring with a force constant 16.0 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 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.)

I've already found:

the period of the gliders motion is 1.57 seconds

maximum value its speed is .124m/s

maximum value of its acceleration is .496m/s^2

Explanation / Answer

Here,

angular frequency , w = sqrt(k/m)

w = sqrt(16/1)

w = 4 rad/s

Now , for the position fuction

x = - A * cos(w * t)

x = - 3.1 * cos(4 * t) cm

for the velocity vector

v = v0 * sin(w * t)

v = 0.124 * sin(4 * t) m/s

for the acceleration vector

a = a0 * cos(w * t)

a = 0.496 * cos(4 * t) m/s^2

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