Experimental Analysis: Forced Harmonic Motion and Resonance

Thread starter VSKA
Start date Apr 10, 2021
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Analysis Experimental Harmonic Harmonic motion Motion Resonance

In summary, forced harmonic motion is when an external force is applied to a system, causing it to oscillate at a specific frequency. Resonance occurs when the frequency of the external force matches the natural frequency of the system, resulting in a significant increase in amplitude. Free harmonic motion occurs without any external force, while forced harmonic motion is caused by an external force. To analyze forced harmonic motion experimentally, one would measure the amplitude and frequency of the oscillations at different external force frequencies and plot the data on a graph. Forced harmonic motion and resonance can be observed in various real-life systems, including musical instruments, bridges, and electronic circuits, and understanding these phenomena is essential for designing and maintaining these systems.

Apr 10, 2021

VSKA

Homework Statement: First of all I would like to clarify that I don't live in an English-speaking country, which means that certain nomenclatures and symbols may be different and may make it difficult to understand, so if you are unable to understand something, I will be happy to help.

Regarding the exercise itself, I need help mainly with questions 3 and 4 that I sent in the original format (excel), as I am not sure if the file will work I am sending images too.

Relevant Equations: The exercise is based on an experiment consisting of a spring-mass system connected to a motor, the goal is to gradually increase the rotation of the motor until the spring enters resonance while amplitude and time data are collected.

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Apr 10, 2021

haruspex

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The expression you are given for A(ω_F) in qn 3 is wrong. The square root in the denominator should extend right across.
##\sqrt{(\omega_0^2-\omega_F^2)^2}+4\gamma^2\omega_F^2## would obviously reduce to ##{|\omega_0^2-\omega_F^2|}+4\gamma^2\omega_F^2##.
It should be ##\sqrt{(\omega_0^2-\omega_F^2)^2+4\gamma^2\omega_F^2}##.
Can you take it from there?

Last edited: Apr 10, 2021

FAQ: Experimental Analysis: Forced Harmonic Motion and Resonance

What is forced harmonic motion?

Forced harmonic motion is a type of motion that occurs when a system is subjected to an external force or driving force that causes it to oscillate at a specific frequency. This frequency is determined by the properties of the system and the frequency of the external force.

What is resonance?

Resonance is a phenomenon that occurs when a system is forced to vibrate at its natural frequency. This results in a large amplitude of oscillation and can cause the system to become unstable if the external force is too strong.

How is forced harmonic motion and resonance studied experimentally?

To study forced harmonic motion and resonance experimentally, a system is set up with a driving force and its response is measured using sensors such as accelerometers or displacement sensors. The frequency of the driving force is varied and the amplitude of the system's response is recorded to determine its natural frequency and resonant frequency.

What are some real-world applications of forced harmonic motion and resonance?

Forced harmonic motion and resonance have many applications in engineering and physics. Some examples include tuning musical instruments, designing earthquake-resistant buildings, and creating efficient suspension systems for vehicles.

How can resonance be avoided or controlled?

To avoid or control resonance, engineers and scientists can adjust the properties of a system, such as its mass and stiffness, to change its natural frequency. Damping can also be added to a system to dissipate energy and reduce the amplitude of oscillation. Additionally, avoiding driving a system at or near its resonant frequency can prevent unwanted resonance.