Oscillation:Resonant frequency in vacuum

[a150daysflood]

Homework Statement

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.

Homework Equations

The Attempt at a Solution

This is the answer.I have googled it and still need explanation 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

 

[Moetasim]

The concept of resonant frequency refers to the natural frequency at which an object or system vibrates with maximum amplitude. In a vacuum, there is no air resistance or other external forces to dampen the oscillation, so the pendulum will continue to oscillate at its natural frequency with an increasing amplitude. As the amplitude increases, the energy of the oscillation also increases, leading to the pendulum reaching higher and higher points before returning back to its starting position. This can be seen in the graph, where the amplitude of the oscillation increases as the frequency approaches the resonant frequency in vacuum. Ultimately, the amplitude would tend to infinity in a perfect vacuum with no external forces acting on the pendulum.