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A mass m is attached to a spring of spring constant k. If the mass is displaced

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Question: A mass m is attached to a spring of spring constant k. If the mass is displaced by a distance x from its equilibrium position, what is the restoring force acting on the mass?

Options:

  1. kx
  2. -kx
  3. mg
  4. -mg

Correct Answer: -kx

Solution: 

The restoring force in simple harmonic motion is given by Hooke\'s law, which states that the force is proportional to the displacement and acts in the opposite direction. Therefore, the restoring force is -kx.

A mass m is attached to a spring of spring constant k. If the mass is displaced

Practice Questions

Q1
A mass m is attached to a spring of spring constant k. If the mass is displaced by a distance x from its equilibrium position, what is the restoring force acting on the mass?
  1. kx
  2. -kx
  3. mg
  4. -mg

Questions & Step-by-Step Solutions

A mass m is attached to a spring of spring constant k. If the mass is displaced by a distance x from its equilibrium position, what is the restoring force acting on the mass?
  • Step 1: Understand that a mass m is attached to a spring.
  • Step 2: Know that the spring has a spring constant k, which measures how stiff the spring is.
  • Step 3: Recognize that when the mass is displaced by a distance x from its resting position, the spring will try to pull it back.
  • Step 4: Remember Hooke's law, which states that the force exerted by a spring is proportional to the distance it is stretched or compressed.
  • Step 5: The formula for Hooke's law is F = -kx, where F is the restoring force, k is the spring constant, and x is the displacement.
  • Step 6: The negative sign indicates that the force acts in the opposite direction of the displacement.
  • Hooke's Law – The principle that the restoring force of a spring is proportional to the displacement from its equilibrium position and acts in the opposite direction.
  • Simple Harmonic Motion – The motion of an object where the restoring force is directly proportional to the displacement and acts towards the equilibrium position.
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