# Oscillation:Resonant frequency in vacuum

• a150daysflood
In summary: I suppose) it breaksIn summary, a pendulum made of a light thread and a low density polystyrene bob is forced to oscillate at different frequencies in air. The resonant frequency, when applied at just the right time, causes the amplitude of the pendulum to increase without interfering with its periodic motion, potentially causing it to increase infinitely.
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.

## 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!

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

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.

## 1. What is oscillation?

Oscillation is a repetitive movement or variation between two points or states. In physics, it refers to the back-and-forth motion of an object or system around a fixed point or equilibrium.

## 2. What is resonant frequency in vacuum?

Resonant frequency in vacuum refers to the natural frequency at which an object or system will vibrate with the greatest amplitude when no external forces are acting on it. In other words, it is the frequency at which the object will resonate or "ring" the most without any damping.

## 3. How is resonant frequency in vacuum calculated?

The formula for calculating resonant frequency in vacuum is f = 1/(2π√(LC)), where f is the frequency in hertz (Hz), L is the inductance in henries (H), and C is the capacitance in farads (F). This formula is derived from the equation of motion for a simple harmonic oscillator.

## 4. What is the significance of resonant frequency in vacuum?

Resonant frequency in vacuum is significant because it allows us to predict and control the behavior of oscillating systems. It is used in various applications such as radio communication, electrical circuits, and musical instruments.

## 5. How does resonant frequency in vacuum differ from resonant frequency in a medium?

Resonant frequency in vacuum is the frequency at which an object will naturally resonate in a vacuum with no external forces. Resonant frequency in a medium, on the other hand, takes into account the effects of the medium on the oscillating system. This can include factors such as air resistance, which can affect the frequency at which an object resonates.

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