Consider a spring-mass oscillator on a train moving at relativistic speed. According to SR, to a stationary observer, both the mass and the period will appear to have increased by a factor of γ. But the period is supposed to be proportional to the square root of the mass. Something is wrong. Don't talk about longitudinal and transverse masses; I can orient the oscillator any way I want. Don't talk about the mass oscillating at relativistic speed; I can keep the oscillation slow.