Question

The equation v =−2.24·sin(9.02t) describes the velocity of a 157g (0.157kg) mass suspended on a spring.

What is the spring constant?

Answer 1

\[ |v_{max}| = 2.24 m/s;
\\ \ \ \ 9.02 t = n \pi /2
\\ \
\\ t = n \frac{ \pi}{18.04/s} \ \ \textrm{at integer values of n, mag. of velocity is max at these times}
\\ \
\\ \textrm{so this can give max kinetic energy of block. At v = 0, max. potential for spring.}
\\ \
\\ v_{min} = 0
\\ 9.02 t = n \pi
\\ \
\\ t = n\frac{\pi}{9.02 /s} \ \textrm{at these times, v = 0}
\\ \
\\ \
\\
\\ v = \frac{dx}{dt}
\\ \
\\ \int dx = - \int2.24 \sin(9.02t)dt
\]

Find x as a function of time, then difference between x _v min at the top and x_v_min at the bottom can give you max displacement. conservation of energy after that!