A 1.00-kg glider attached to a spring with a force constant 36.0 N/m oscillates

Question

A 1.00-kg glider attached to a spring with a force constant 36.0 N/m oscillates on a frictionless, horizontal air track. At t = 0, the glider is released from rest at x = -2.60 cm (that is, the spring is compressed by 2.60 cm).

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

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

speed = in m/s

acceleration = in m/s^2

(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.)

x(t)=

v(t)=

a(t)=

Explanation / Answer

m = mass of the glider = 1 kg
k = spring constant = 36 N/m
d = initial position (at time t=0) = -0.026 m

The angular frequency is:
? = ?( k / m )
? = ?( (36 N/m) / (1 kg) )
? = 6 rad/s

t = 2*pi/w = 1.046 secs
The amplitude is:
A = |d|
A = 0.026 m

The maximum speed is:
v = A?
v = (0.026 m)(6 rad/s)
v = 0.156 m/s

The maximum acceleration is:
a = A?

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