Answer
See answers.
Work Step by Step
a. The object starts at the maximum, most positive displacement. Its motion is represented by a cosine function. The mass, period, and the amplitude are given.
$$A=0.16\;m$$
$$\omega = \frac{2 \pi}{T}=\frac{2 \pi}{0.45\;s}=13.96\;rad/s$$
$$y=(0.16\;m)cos(14t)$$
b. The time to first reach equilibrium is one-quarter of a period.
$$\frac{1}{4}(0.45 s)=0.11 s$$
c. The maximum speed is calculated using Equation 11–7a.
$$v_{max}=\omega A=(13.96\;rad/s)(0.16\;m)=2.2\;m/s$$
d. The maximum acceleration is calculated using Equation 11–10.
$$a_{max}=\omega^2 A=(13.96\;rad/s)^2(0.16\;m)=31\;m/s^2$$
The maximum acceleration occurs at the endpoints of the motion. It is first attained at the moment of release, when the spring is fully compressed.
