A 492g oscillator has a speed of 99.5cm/s when its displacement is 3.60cm and 72.5cm/s when its displacement is 5.10cm .
What is the oscillator's maximum speed? (units cm/s)
At the maximum speed, the kinetic energy of the oscillating mass equals the total energy, which is
(M/2)*Vmax^2
= (k/2)*(3.6)^2 + (M/2)(99.5)^2
and
(M/2)*Vmax^2
= (k/2)*(5.1)^2 + (M/2)(72.5)^2
You know what M is and have two equations to solve for the unknowns k and Vmax.