How can the speed of oscillation of a harmonic oscillator be affected if somehow it got accelerated to a relativistic speed perpendicular to its oscillation? Can this be compared with the effect on relativistic laser clock?
In the inertial frame of the harmonic oscillator the frequency/speed is not affected. But according to the rest frame, the frequency is lower because of time dilation. In the rest frame, the reduced frequency can be explained by the mass (should rather be called inertia) increasing (see relativistic mass) and the spring constant decreasing.