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Is the motion of a leaf of a tree blowing in the wind periodic?
Is the motion of a leaf of a tree blowing in the wind periodic?
What characteristic does a frictionless horizontal surface provide in the context of simple harmonic motion?
What characteristic does a frictionless horizontal surface provide in the context of simple harmonic motion?
What role does the restoring force play in simple harmonic motion?
What role does the restoring force play in simple harmonic motion?
What is a key requirement for a surface in the context of studying simple harmonic motion with a rectangular block?
What is a key requirement for a surface in the context of studying simple harmonic motion with a rectangular block?
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What type of motion does a rectangular block on a frictionless surface exhibit when attached to a spring?
What type of motion does a rectangular block on a frictionless surface exhibit when attached to a spring?
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What is used to measure displacement in the given motion?
What is used to measure displacement in the given motion?
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In the equilibrium position, what force does the spring exert on the block?
In the equilibrium position, what force does the spring exert on the block?
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When the block is displaced towards the right from the equilibrium position, in which direction is the restoring force exerted by the spring?
When the block is displaced towards the right from the equilibrium position, in which direction is the restoring force exerted by the spring?
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What characteristic of the spring is responsible for the restoring force?
What characteristic of the spring is responsible for the restoring force?
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What is the nature of the restoring force in relation to displacement?
What is the nature of the restoring force in relation to displacement?
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What does the force constant (k) depend on?
What does the force constant (k) depend on?
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What does the negative sign in the equation $f = -kx$ indicate?
What does the negative sign in the equation $f = -kx$ indicate?
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In which direction is the force exerted by the spring if the block is displaced to the left of its equilibrium position?
In which direction is the force exerted by the spring if the block is displaced to the left of its equilibrium position?
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How is the acceleration (a) of the block related to the displacement (x)?
How is the acceleration (a) of the block related to the displacement (x)?
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What happens to the block's speed as it moves towards the mean position?
What happens to the block's speed as it moves towards the mean position?
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Where does the block come to rest in the context of the given motion?
Where does the block come to rest in the context of the given motion?
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What is the equation of motion for a simple harmonic oscillator?
What is the equation of motion for a simple harmonic oscillator?
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In simple harmonic motion, what is the speed of the block at the mean position?
In simple harmonic motion, what is the speed of the block at the mean position?
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In which scenario is the force on the block zero?
In which scenario is the force on the block zero?
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What happens to the displacement of the block as it moves toward the mean position in simple harmonic motion?
What happens to the displacement of the block as it moves toward the mean position in simple harmonic motion?
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What is the expression for the force on the block when the spring is stretched?
What is the expression for the force on the block when the spring is stretched?
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What is the relationship between force and displacement in simple harmonic motion?
What is the relationship between force and displacement in simple harmonic motion?
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What kind of motion does the block exhibit in a spring mass oscillator system?
What kind of motion does the block exhibit in a spring mass oscillator system?
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When the block returns to its mean position, what is the value of its acceleration in simple harmonic motion?
When the block returns to its mean position, what is the value of its acceleration in simple harmonic motion?
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What defines the equilibrium position of the spring mass oscillator?
What defines the equilibrium position of the spring mass oscillator?
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What causes the block to come to rest at the extreme left position in simple harmonic motion?
What causes the block to come to rest at the extreme left position in simple harmonic motion?
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Which of the following scenarios corresponds to the spring being compressed?
Which of the following scenarios corresponds to the spring being compressed?
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In the context of the spring mass oscillator system, what does the spring constant 'k' represent?
In the context of the spring mass oscillator system, what does the spring constant 'k' represent?
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What is the defining characteristic of linear simple harmonic motion?
What is the defining characteristic of linear simple harmonic motion?
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What happens to the speed of the block as it approaches the mean position?
What happens to the speed of the block as it approaches the mean position?
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In a complete oscillation, the object:
In a complete oscillation, the object:
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What governs the motion of the block if there is friction between the block and the resting surface?
What governs the motion of the block if there is friction between the block and the resting surface?
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How does the restoring force behave at the maximum displacement from the mean position?
How does the restoring force behave at the maximum displacement from the mean position?
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What type of motion does a hydrometer exhibit when it is depressed and released in a liquid?
What type of motion does a hydrometer exhibit when it is depressed and released in a liquid?
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Study Notes
Linear Simple Harmonic Motion (SHM)
- Linear Simple Harmonic Motion (SHM) occurs when a block is attached to a spring and oscillates back and forth on either side of its equilibrium position.
- The block is pulled to the right and released, and the spring exerts a restoring force on the block, causing it to oscillate.
- There are three scenarios: Stretched, Relaxed, and Compressed.
- The force on the block is F = -kx, where k is the spring constant and x is the displacement from the equilibrium position.
Remember this
- For SHM, displacement is always measured from the mean position.
- The entire motion occurs on either side of the equilibrium position.
Equation of Motion
- The equation of motion for SHM is f = -kx, where k is the spring constant and x is the displacement from the equilibrium position.
- The negative sign indicates that the force and displacement are oppositely directed.
Force Exerted by a Spring
- If the block is displaced towards the left of its equilibrium position, the force exerted on the block is directed towards the right and its magnitude is proportional to the displacement from the mean position.
Acceleration of the Block
- The acceleration of the block is a = - (k/m)x, where m is the mass of the block.
- The acceleration is also proportional to the displacement, and its direction is opposite to that of the displacement.
Block's Motion
- As the block moves towards the mean position, its speed increases due to its acceleration, but its displacement from the mean position decreases.
- When the block returns to its mean position, its displacement and hence force and acceleration are zero.
- The speed of the block at the mean position becomes maximum, and its kinetic energy attains its maximum value.
Simple Harmonic Motion
- Simple harmonic motion is a type of linear periodic motion where the force (or acceleration) is always directed towards the mean position and its magnitude is proportional to the displacement from the mean position.
- The block oscillates back and forth around the mean position, with its speed increasing and decreasing as it moves towards and away from the mean position.
Conditions for Simple Harmonic Motion
- A complete oscillation is when the object goes from one extreme to the other and back to the initial position.
- The conditions required for simple harmonic motion are:
- Force (or acceleration) is always directed towards the mean position.
- The magnitude of the force (or acceleration) is proportional to the displacement from the mean position.
Examples of Simple Harmonic Motion
- A hydrometer depressed and released in a liquid performs linear simple harmonic motion.
- A U-tube filled with a liquid, where the column of mercury in one arm is the same as that in the other arm, performs simple harmonic motion when released and starts moving up and down.
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Description
Understand the concept of simple harmonic motion (SHM) and determine if the motion of a leaf blowing in the wind is periodic. Learn about the restoring force in SHM.
