1) A simple harmonic oscillator has a potential energy of 25x2 Joules, a kinetic energy of 0.5v2 Joules where x is the displacement in meters and v the instantaneous velocity in m/s. The oscillator is set in motion with a total energy of 0.25 Joules. Determine the values of:
a) the amplitude
b) the maximum instantaneous velocity
c) the angular frequency,and
d) explain why increasing the amplitude does not change the frequency (don't give a trivial answer such as "because the amplitude is not in the formula for frequency").