The question is not as silly as it looks, actually. Oscillations are present in many physical processes and sometimes they can have impressive consequences. They occur not only in physical systems but also in biological systems and in human society.
For example, earthquakes are one of the most destructive oscillations known to man. They result from the sudden release of stored energy in the Earth's crust that creates seismic waves, they are often felt as vibrations of the ground.
Smaller earthquakes can also be caused by volcanic activity, landslides, mine blasts and nuclear tests. In its most generic sense, the word earthquake is used to describe any seismic event-whether a natural phenomenon or an event caused by humans-that generates seismic waves.
But could people really cause an earthquake just by jumping around? Standing next to a massive person while he jumps, one can sense a small tremble. What could happen if the entire population of China were to jump in the same time? China has an estimated population of 2.3 billions, so they should make an impact, right?
To test that idea, the creators of a science program on German television asked themselves what would happen if the entire Chinese population engaged in synchronized hopping and enlisted the help of a rock band, to perform a small scale experiment.
During a German music festival called Rock at the Ring, the band We Are Heroes told the thousands of rock fan/hoppers (total attendance 50,000) to jump, while the program's crew recorded the event on videotape and the Potsdam Geological Research Center recorded it on seismometers.
The results were...disappointing. "A seismometer measured four oscillations per second, while the earth moved only one-twentieth of a millimeter. "We showed that people cannot start a (real) earthquake by hopping," remarks Ulrich Gruenwald, producer of the program.
Well, the oscillations themselves are not as damaging as one particular effect, the resonance. Maybe the entire population of China wouldn't cause an earthquake just by jumping once, but if their jumps were to resonate, the effects could be much greater.
It's a known fact that resonance can destroy bridges and buildings, the most famous example being an army marching over a bridge, that breaks up the march, even if they're not absolutely sure it would collapse the bridge.
So, it seems that these applications proved that in the case of the planet, no, a bunch of people marching around aren't going to cause it to vibrate.