An oscillating mass at the end of a spring is at a distance $y$ from its equilibrium position given by $\displaystyle y = A \, \sin\left( \sqrt{\frac{k}{m}} \cdot t \right)$. The constant $k$ measures the stiffness of the spring.

Find the first positive time time $t_1$ at which the mass is farthest from its equilibrium position: $t_1 =$

Find the first positive time $t_2$ at which the mass is moving fastest: $t_2 =$

Find the first positive time $t_3$ at which the mass has the largest acceleration (in magnitude): $t_3 =$

What is the period, $T$, of the oscillation? $T =$

Find $dT/dm$: ${dT\over dm} =$
(What does the sign of $dT/dm$ tell you?)