In a simple harmonic motion, the maximum speed is given by:
[tex] v_{max}=\omega A [/tex]
where [tex] \omega [/tex] is the angular frequency and A is the amplitude of the motion, while the maximum acceleration is given by
[tex] a_{max}=\omega^2 A [/tex]
The problem tells us both the values of the maximum speed, [tex] v_{max}=3 m/s [/tex], and the maximum acceleration, [tex] a_{max}=15 m/s^2 [/tex], so we can write the following equations:
[tex] \omega A=3 [/tex]
[tex] \omega^2 A=15 [/tex]
and the solutions are [tex] \omega=5 rad/s [/tex], [tex] A=\frac{3}{5}m [/tex].
We are only interested in the angular frequency; in fact, we can find the period of the motion by using the equation:
[tex] T=\frac{2 \pi}{\omega}=\frac{2 \pi}{5 rad/s}=1.26 s [/tex]
