A mass hanging from the end of a spring has a phase rate of $\omega=6.3 \mathrm{~s}^{-1} \approx 1$ cycle/s. Let's define $t=0$ to be when the mass passes $x=0$ going up. If its speed as it passes is $1.0 \mathrm{~m} / \mathrm{s}$, what is its amplitude $A$ ?
A) 0
B) $\mathbf{0 . 1 6} \mathrm{m}$
C) $1.0 \mathrm{~m}$
D) $6.3 \mathrm{~m}$
E) We are not given enough information to answer.
F) Some other result (specify)

Question

Quizplus · Accepted Answer

The amplitude $A$ can be found using the relationship between the maximum speed $v_{max}$, the angular frequency $\omega$, and the amplitude $A$, which is given by $v_{max} = \omega A$. Given that the speed as it passes $x=0$ is $1.0 \mathrm{~m/s}$ and $\omega = 6.3 \mathrm{~s}^{-1}$, we can solve for $A$ as $A = \frac{v_{max}}{\omega} = \frac{1.0}{6.3} \approx 0.16 \mathrm{~m}$.

A Mass Hanging from the End of a Spring Has ω=6.3 s−1≈1\omega=6.3 \mathrm{~s}^{-1} \approx 1ω=6.3 s−1≈1

A Mass Hanging from the End of a Spring Has $\omega=6.3 \mathrm{~s}^{-1} \approx 1$