Oscillation:Resonant frequency in vacuum

[a150daysflood]

1. The problem statement, all variables and given/known data
A pendulum is constructed from a fixed length of light thread and and a spherical,low density,polystyrene bob.It is forced to oscillate at a different frequencies in air,and the response is shown in the graph below.
http://elearn.litespeed.com.sg/Elearning_Platform/Learning_Objects/125/149/363990__image527058.jpg

2. Relevant equations



3. The attempt at a solution

http://elearn.litespeed.com.sg/Elearning_Platform/Learning_Objects/129/149/363990__image527062.jpg
This is the answer.I have googled it and still need explaination regarding how does ringing something at resonant frequency in vacuum causes the amplitude to tend to infinity.

Thanks for your help!

[blochwave]

Well that's basically what the resonant frequency is

Don't take this too literally as it's not quite the exact same thing, but to help understand resonance, let's say I'm pushing you on a swing. So I'm applying a periodic force at some frequency and you're oscillating back and forth. What happens if I apply the force too early while you're still coming back at me? Do I increase your amplitude? No you knock me on my butt. What if I wait too long? I fall on my face

But what if I apply the force at jussst the right time? I increase your amplitude. So if you're applying the force at just the right times (the resonant frequency) to the pendulum bob, you increase its amplitude every time without screwing up its own periodic motion, so it increases and increases