How Do Driven Vibrations Impact a Seismometer?

[eng.physicsbr]

Hello guys, this question showed up in my test last week as a challenge question, but the problem is, I'm the first year at college and have not yet learned to solve differential equations. Of course I did not manage to do it but I´m pretty eager to learn. Thanks in advance

 

[RACHI]

Gosh, I had a similar test last year and it was very hard to figure out.