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Questions and Answers
What is the characteristic of periodic motion?
What is the term for motion when the force acting on the object is proportional to the position of the object relative to some equilibrium position?
What happens to the restoring force when the block is displaced to the right of x = 0?
What is the force described by Hooke’s Law?
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What is the relationship between force and displacement in Hooke’s Law?
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What does a positive position indicate in a spring-mass system?
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What does a negative position indicate in a spring-mass system?
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What happens to the restoring force when the block is at the equilibrium position?
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What is the net force described by Hooke’s Law in terms of acceleration?
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What does Hooke’s Law state about the relationship between force and displacement?
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What type of motion occurs when the acceleration is proportional to the position and oppositely directed to the displacement from equilibrium?
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In simple harmonic motion, what happens when the block passes through the equilibrium position?
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What is the mathematical representation of acceleration in simple harmonic motion?
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What function satisfies the equation for simple harmonic motion's acceleration?
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What is the amplitude of the motion in simple harmonic motion?
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What is the phase constant or the initial phase angle in simple harmonic motion?
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What happens to the phase of the motion if a particle is at $x = A$ at $t = 0$ in simple harmonic motion?
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Study Notes
Characteristics of Periodic Motion
- Periodic motion has a constant period and amplitude
- The motion repeats itself after a fixed interval of time
Simple Harmonic Motion (SHM)
- SHM occurs when the force acting on an object is proportional to its position relative to an equilibrium position
- The force described by Hooke's Law is the restoring force
- The force is proportional to the displacement from the equilibrium position
Hooke's Law
- The relationship between force and displacement is F = -kx, where k is the spring constant
- The negative sign indicates that the force is opposite in direction to the displacement
Spring-Mass System
- A positive position indicates the block is displaced to the right of x = 0
- A negative position indicates the block is displaced to the left of x = 0
- At the equilibrium position, the restoring force is zero
Acceleration in SHM
- The net force is described by the equation F = -kx = ma, where m is the mass and a is the acceleration
- The acceleration is proportional to the position and oppositely directed to the displacement from equilibrium
Simple Harmonic Motion
- When the block passes through the equilibrium position, the velocity is maximum and the acceleration is zero
- The mathematical representation of acceleration is a = -ω²x, where ω is the angular frequency
- The function that satisfies the equation for SHM acceleration is x(t) = A cos(ωt + φ)
- The amplitude of the motion is A
- The phase constant or initial phase angle is φ
- If a particle is at x = A at t = 0, the phase of the motion is zero
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Description
Test your knowledge on the concepts of periodic motion, including simple harmonic motion and the motion of a spring-mass system. Explore questions related to the regular repetition of object motion and its relation to equilibrium position and force.
