Period for harmonic motion (horizontal)

In summary, a period for harmonic motion (horizontal) is the time it takes for an object to complete one full cycle of its motion and is represented by the symbol T. It can be calculated using the equation T = 2π√(m/k) and is affected by factors such as mass, spring constant, and amplitude. Frequency and period are inversely related, and the period can be altered by changing these factors or external factors such as friction.
  • #1
hms.tech
247
0
Consider a light flexible rod placed on a horizontle table with part of the rod (length say "x") hanging freely (ie without support of the table) see attachment for clarity

A mass is also hung from the rod t one end.

Are there any equations that relate the Period T of the end of the rod to the length "x" , and the mass(hanging) ?
 

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  • #2
Look up "cantilever with end mass frequency".
 

Related to Period for harmonic motion (horizontal)

What is a period for harmonic motion (horizontal)?

A period for harmonic motion (horizontal) refers to the amount of time it takes for an object to complete one full cycle of its motion. It is typically measured in seconds and is represented by the symbol T.

How is the period for harmonic motion (horizontal) calculated?

The period for harmonic motion (horizontal) can be calculated using the equation T = 2π√(m/k), where T is the period, π is pi, m is the mass of the object, and k is the spring constant. This equation applies to objects undergoing simple harmonic motion, where the restoring force is directly proportional to the displacement from the equilibrium position.

What factors affect the period for harmonic motion (horizontal)?

The period for harmonic motion (horizontal) is affected by the mass of the object, the spring constant, and the amplitude (maximum displacement) of the motion. As the mass increases, the period also increases. Similarly, as the spring constant increases, the period decreases. The period also increases as the amplitude increases.

What is the relationship between frequency and period for harmonic motion (horizontal)?

Frequency and period are inversely related for harmonic motion (horizontal). This means that as the period increases, the frequency decreases and vice versa. The relationship between frequency (f) and period (T) can be represented by the equation f = 1/T.

Can the period for harmonic motion (horizontal) be altered?

Yes, the period for harmonic motion (horizontal) can be altered by changing the factors that affect it, such as the mass, spring constant, and amplitude. Additionally, external factors such as friction can also affect the period of harmonic motion.

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