A 1.00-kg glider attached to a spring with a force constant 16.0 N/m oscillates
ID: 1605719 • Letter: A
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 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.)
Explanation / Answer
given
m = 1 kg
k = 16 N/m
A = 3.1 cm = 0.031 m
a) angular frequency, w = sqrt(k/m) = sqrt(16/1) = 4 rad/s
T = 2*pi/w
= 2*pi/4
= 1.57 s
b) Vmax = A*w
= 0.031*4
= 0.124 m/s
a_max = A*w^2
= 0.031*4^2
= 0.496 m/s^2
c)
x(t) = -A*cos(w*t)
= -0.031*cos(4*t)
v(t) = dx/dt
= A*w*sin(w*t)
= 0.031*4*sin(4*t)
= 0.124*sin(4*t)
a(t) = dv/dt
= A*w^2*cos(w*t)
= 0.496*cos(4*t)
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