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What is simple harmonic motion?
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Simple harmonic motion is a type of periodic motion where the restoring force is directly proportional to the displacement and acts in the direction opposite to that of displacement.
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What is a mathematical pendulum?
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A mathematical pendulum is a simple theoretical model consisting of a mass attached to a string or rod of fixed length, where the forces of gravity and tension act on the mass.
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What equation describes the period of a mathematical pendulum?
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The period T of a mathematical pendulum is given by the equation T = 2π√(L/g), where L is the length of the pendulum and g is the acceleration due to gravity.
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How does the amplitude affect the period of a mathematical pendulum?
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For small amplitudes, the amplitude does not affect the period, allowing it to be approximated as isochronous. However, larger amplitudes cause deviations from this approximation.
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What factors influence the oscillation period of a spring pendulum?
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The oscillation period of a spring pendulum is influenced by the mass attached to the spring and the spring constant, but not by the amplitude of oscillation.
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What is Hooke's Law?
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Hooke's Law states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position, F = -kx, where k is the spring constant and x is the displacement.
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Define the term 'spring constant'.
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The spring constant, denoted by k, is a measure of a spring's stiffness. It indicates how much force is needed to stretch or compress the spring by a unit length.
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What is the formula for the period of a spring pendulum?
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The period T of a spring pendulum is given by T = 2π√(m/k), where m is the mass attached to the spring, and k is the spring constant.
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How do you calculate the restoring force in a harmonic oscillation?
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The restoring force F in simple harmonic motion is calculated using F = -kx for a spring pendulum or F = -mg sin(θ) for a small angle in a mathematical pendulum.
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What role does gravity play in a pendulum's motion?
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Gravity acts as the restoring force in a pendulum's motion, pulling the pendulum back towards its equilibrium position.
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What defines the equilibrium position in a pendulum's motion?
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The equilibrium position is the point in the pendulum's motion where the net force on the pendulum is zero, typically where it hangs directly downward at rest.
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Compare damped and undamped oscillations.
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Undamped oscillations occur when amplitude remains constant over time, while damped oscillations experience gradually reducing amplitude due to energy loss through friction or air resistance.
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What is the difference between forced and natural frequency?
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Natural frequency is the frequency at which a system oscillates when not disturbed by an external force, while forced frequency is the frequency of oscillation when influenced by an external force.
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What effect does changing the length of a pendulum have on its period?
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Increasing the length of a pendulum increases its period, causing it to swing more slowly, while shortening the length decreases the period, increasing the speed of the swing.
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Why do pendulums exhibit simple harmonic motion only at small angles?
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At small angles, the approximations sin(θ) ≈ θ hold true, allowing the restoring force to be proportional to the displacement, a requirement for simple harmonic motion.
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