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Questions and Answers
A pendulum is an object that is attached to a fixed point so it can swing freely.
A pendulum is an object that is attached to a fixed point so it can swing freely.
True
Pendulums are often used in regulating pendulum clocks due to their irregular motion.
Pendulums are often used in regulating pendulum clocks due to their irregular motion.
False
In a simple gravity pendulum, the weight is attached to a string with mass.
In a simple gravity pendulum, the weight is attached to a string with mass.
False
The restoring force of a pendulum will accelerate it away from the equilibrium position.
The restoring force of a pendulum will accelerate it away from the equilibrium position.
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A simple pendulum assumes that the string on which the bob swings is massless and remains slack.
A simple pendulum assumes that the string on which the bob swings is massless and remains slack.
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The natural frequency of a pendulum depends on the mass of the pendulum.
The natural frequency of a pendulum depends on the mass of the pendulum.
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The equation T=2π/ω gives the time of one cycle (period) of a pendulum in seconds.
The equation T=2π/ω gives the time of one cycle (period) of a pendulum in seconds.
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The equation Τ = 2π √l/g gives the natural frequency of a pendulum in rad/sec.
The equation Τ = 2π √l/g gives the natural frequency of a pendulum in rad/sec.
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The equation Τ² = 4π² L/g shows that the period of a pendulum is inversely proportional to its length.
The equation Τ² = 4π² L/g shows that the period of a pendulum is inversely proportional to its length.
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Motion in a simple pendulum occurs in three dimensions.
Motion in a simple pendulum occurs in three dimensions.
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Study Notes
Simple Pendulum Experiment
- The experiment aims to validate the simple pendulum theory and estimate the gravitational acceleration, g.
What is a Pendulum?
- A pendulum is an object attached to a pivot point, allowing it to swing freely.
- It is subject to a restoring force that accelerates it towards an equilibrium position.
- When displaced from its rest position, the restoring force causes the pendulum to oscillate about the equilibrium position.
Simple Gravity Pendulum (Bob Pendulum)
- A weight (or bob) is attached to a massless string.
- When given an initial push, it swings back and forth under the influence of gravity around its central (lowest) point.
- The regular motion of pendulums can be used for time keeping, and pendulums are used to regulate pendulum clocks.
Assumptions of a Simple Pendulum
- The rod/string/cable is massless and always remains taut.
- Motion occurs in a plane.
Equations of Motion
- T = 2π/ω (where T is the time of one cycle or period in seconds, and ω is the natural frequency in rad/sec)
- ω = √g/l
- T = 2π √l/g
- T² = 4π² L/g (where L is the length of the string)
Key Facts
- The natural frequency is a function of the string length and does not depend on the mass of the pendulum.
- The period of oscillation is proportional to the square root of the length of the string.
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Description
Learn about the validation of simple pendulum theory and the estimation of gravitational acceleration through this experiment. Understand how a pendulum swings freely around a pivot point, subject to a restoring force that causes it to oscillate about an equilibrium position.
