# What is the effect of mass on resonance amplitude?

When a system is undergoing forced oscillations, why does reducing the mass of the system cause the frequency response curve to shift downwards? I encountered this problem in a practice paper, but I can't seem to put my head around the model answer. I get that reducing the mass causes the natural frequency to increase, so the resonance frequency becomes higher, but why does the amplitude of oscillation decrease across all frequencies?

• See en.wikipedia.org/wiki/… and the solution for driven oscillators. There you see that the amplitude is damped by an exponential decrasing which is stronger if the mass is smaller. Aug 11, 2018 at 13:12
• But what if the system is not damped? Aug 11, 2018 at 13:19
• Look at cts.iitkgp.ac.in/home/pratik/forcednew.pdf for it. Then the amplitude $A = \frac{F}{m(\omega_0^2-\omega^2)}$ depends also on the mass $m$ and the force $F$. Aug 11, 2018 at 13:38
• "But what if the system is not damped?" Take the limit of the damped behavior as $b \to 0$ and make your math teacher cry. Real systems, of course always have some damping and will break if you make the driving force sufficiently large in comparison to the damping forces. Aug 11, 2018 at 15:57