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At the equilibrium position O, what is the displacement?
At the equilibrium position O, what is the displacement?
The total energy of the system in simple harmonic motion is always variable.
The total energy of the system in simple harmonic motion is always variable.
False
What occurs to the kinetic energy of the moving mass at the mean position O?
What occurs to the kinetic energy of the moving mass at the mean position O?
It reaches its maximum value.
At the extreme positions A and B, the potential energy is at its ______.
At the extreme positions A and B, the potential energy is at its ______.
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Match the following terms with their definitions:
Match the following terms with their definitions:
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What happens to the energy in a damped oscillation system?
What happens to the energy in a damped oscillation system?
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In free oscillations, the system is negatively impacted by damping forces.
In free oscillations, the system is negatively impacted by damping forces.
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How does the spring behave during the motion in simple harmonic motion?
How does the spring behave during the motion in simple harmonic motion?
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Kinetic energy is at its minimum when the displacement is at its ______.
Kinetic energy is at its minimum when the displacement is at its ______.
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Which factor contributes to the damping of oscillations?
Which factor contributes to the damping of oscillations?
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What is true about the total energy (ET) in simple harmonic motion?
What is true about the total energy (ET) in simple harmonic motion?
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In simple harmonic motion, kinetic energy (KE) equals potential energy (PE) at the mean position.
In simple harmonic motion, kinetic energy (KE) equals potential energy (PE) at the mean position.
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What is the formula to find the periodic time (T) using angular frequency (ω)?
What is the formula to find the periodic time (T) using angular frequency (ω)?
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In the equation 𝑎 = −𝜔²𝑥, the negative sign shows that the acceleration is __________ to the displacement.
In the equation 𝑎 = −𝜔²𝑥, the negative sign shows that the acceleration is __________ to the displacement.
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Match the following energy forms with their descriptions in simple harmonic motion:
Match the following energy forms with their descriptions in simple harmonic motion:
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What does the gradient (m) represent in the context of acceleration-displacement graph?
What does the gradient (m) represent in the context of acceleration-displacement graph?
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Which of the following is an example of Simple Harmonic Motion?
Which of the following is an example of Simple Harmonic Motion?
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In Simple Harmonic Motion, the restoring force increases as the mass approaches the equilibrium position.
In Simple Harmonic Motion, the restoring force increases as the mass approaches the equilibrium position.
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What happens to the mass when it is pulled to position A and released?
What happens to the mass when it is pulled to position A and released?
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The oscillation in Simple Harmonic Motion can be described as going from position O to position A to position B and back to position O. This sequence is known as one __________.
The oscillation in Simple Harmonic Motion can be described as going from position O to position A to position B and back to position O. This sequence is known as one __________.
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Match the following terms related to Simple Harmonic Motion to their definitions:
Match the following terms related to Simple Harmonic Motion to their definitions:
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According to Hooke's Law, what happens to the force as the extension decreases?
According to Hooke's Law, what happens to the force as the extension decreases?
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The mass in Simple Harmonic Motion comes to rest at position A.
The mass in Simple Harmonic Motion comes to rest at position A.
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Define Simple Harmonic Motion.
Define Simple Harmonic Motion.
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In the context of Simple Harmonic Motion, the term __________ refers to the distance the spring is stretched or compressed from its natural length.
In the context of Simple Harmonic Motion, the term __________ refers to the distance the spring is stretched or compressed from its natural length.
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What is the primary characteristic of the motion observed in a simple pendulum?
What is the primary characteristic of the motion observed in a simple pendulum?
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What does the equation $F = k \Delta l$ represent in the context of simple harmonic motion?
What does the equation $F = k \Delta l$ represent in the context of simple harmonic motion?
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In simple harmonic motion, acceleration and displacement are always in the same direction.
In simple harmonic motion, acceleration and displacement are always in the same direction.
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What does $\omega$ represent in the context of simple harmonic motion?
What does $\omega$ represent in the context of simple harmonic motion?
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In simple harmonic motion, the restoring force is directly proportional to the displacement, denoted as $F \propto -______ $.
In simple harmonic motion, the restoring force is directly proportional to the displacement, denoted as $F \propto -______ $.
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Which of the following statements about simple harmonic motion is true?
Which of the following statements about simple harmonic motion is true?
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In simple harmonic motion, the potential energy is independent of displacement.
In simple harmonic motion, the potential energy is independent of displacement.
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What is the relationship between acceleration ($a$) and displacement ($x$) in simple harmonic motion?
What is the relationship between acceleration ($a$) and displacement ($x$) in simple harmonic motion?
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The equation for acceleration in S.H.M. can be represented as $a = -______^2 x$.
The equation for acceleration in S.H.M. can be represented as $a = -______^2 x$.
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Which relationship best describes kinetic energy in simple harmonic motion?
Which relationship best describes kinetic energy in simple harmonic motion?
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What does the amplitude 𝐴 represent in oscillations?
What does the amplitude 𝐴 represent in oscillations?
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The periodic time 𝑇 is equal to the inverse of frequency 𝑓.
The periodic time 𝑇 is equal to the inverse of frequency 𝑓.
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What is the formula for the angular frequency 𝜔 in terms of the frequency 𝑓?
What is the formula for the angular frequency 𝜔 in terms of the frequency 𝑓?
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The acceleration of a body in simple harmonic motion is given by 𝑎 = −𝜔²______.
The acceleration of a body in simple harmonic motion is given by 𝑎 = −𝜔²______.
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Match the types of energy with their locations in an oscillator's motion:
Match the types of energy with their locations in an oscillator's motion:
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What is the total energy of an oscillator when there are no energy losses?
What is the total energy of an oscillator when there are no energy losses?
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At the equilibrium position, all energy is potential energy.
At the equilibrium position, all energy is potential energy.
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If a body has an acceleration of 4 𝑚/𝑠² when displaced by 4 𝑐𝑚, what is its angular frequency 𝜔²?
If a body has an acceleration of 4 𝑚/𝑠² when displaced by 4 𝑐𝑚, what is its angular frequency 𝜔²?
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The number of oscillations per second is called ______.
The number of oscillations per second is called ______.
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What happens to potential energy (𝑃𝐸) and kinetic energy (𝐾𝐸) during an oscillation?
What happens to potential energy (𝑃𝐸) and kinetic energy (𝐾𝐸) during an oscillation?
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Study Notes
Simple Harmonic Motion (S.H.M.)
- S.H.M. is a back-and-forth motion, like a pendulum, a mass on a spring, or a cork in water.
- A mass attached to a spring demonstrates S.H.M.
- Equilibrium position (O) is the rest position of the mass.
- Restoring force pulls the mass back toward equilibrium as it moves away.
Definition and Equations
- Restoring force is directly proportional to displacement from equilibrium.
- Restoring force acts in the opposite direction of the displacement.
- Hooke's Law: F = kΔl (force is proportional to the displacement)
- Acceleration is directly proportional to the displacement from the equilibrium position (negative sign implies opposite direction).
- Acceleration is a=−ω²x (where ω is angular frequency)
Observations
- The restoring force decreases as the mass approaches equilibrium position.
- The force is proportional to the extension of the spring, so as the extension decreases, force decreases.
- Force is directly proportional to the displacement.
Displacement
- Displacement (x) is the distance of the mass from the equilibrium position.
- Displacement is a vector quantity.
- Maximum displacement is the amplitude (A).
Energy in Simple Harmonic Motion
- Energy of the vibrating system is a combination of potential energy stored in the spring (PE) and the kinetic energy (KE) of the moving mass.
- At maximum displacement, all the energy is stored as potential energy.
- At equilibrium position, all the energy is kinetic energy.
- Total energy (E) remains constant throughout the motion (assuming no energy loss).
Oscillations
- Oscillations can come to a halt because of energy loss to friction.
- Loss of energy in the system through friction causes damping effect.
- Free oscillations are continuous without any damping.
Frequency and Periodic Time
- Frequency (f) is the number of oscillations per second,measured in Hz (or s⁻¹).
- Periodic time (or period) (T) is the time taken for one oscillation and measured in seconds.
- Relationship: f = 1/T and T = (2π)/ω (where ω is angular frequency).
Acceleration-Displacement Graph
- The graph of acceleration (a) against displacement (x) is a parabola.
- The slope of the graph represents the constant −ω².
Angular Frequency
- Angular frequency (ω) is a constant that relates acceleration and displacement in S.H.M.
Summary of Key Formulas
- F = -kx
- a = -ω²x
- f = 1/T
- T = 2π/ω
- ω² = k/m
- E = 1/2 kA² (or E = 1/2 mω²A²)
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Description
Test your knowledge on Simple Harmonic Motion (S.H.M.) including the definition, equations, and key observations. This quiz covers concepts such as Hooke's Law, the restoring force, and acceleration in S.H.M. Perfect for students studying physics concepts related to oscillatory motion.
