12-01 simple harmonic motion

Physics Lesson Plan Goals and Objectives

• Goal(s)/PLO(s):

  • Use appropriate materials to verify Hooke's Law.

  • Relate Hooke's Law to situations in their homes and community.

  • Solve problems using Hooke's Law that involve:

    • Force.

    • Spring constant.

    • Distortion.

Required Materials

• Spring.

• Ring stand.

• Masses.

• Pendulum bob.

• String.

Simple Harmonic Motion

• A periodic motion is defined as a repeated motion.

• Demonstrations:

  • Demo 1: Mass on a spring bouncing up and down

    • Link to Simulation

  • Demo 2: Pendulum swinging back and forth

    • Link to Simulation

• The simplest example of simple harmonic motion is a mass attached to a spring on a horizontal, frictionless surface.

Dynamics of a Mass-Spring System

• At maximum displacement:

  • The force is at its highest, pulling towards equilibrium.

  • The acceleration is also at its highest.

• At equilibrium:

  • The force is zero (no acceleration), but the mass has maximum velocity and tends to overshoot to maximum displacement in the opposite direction.

• In an ideal scenario (frictionless surface), the mass-spring system would oscillate indefinitely.

• Damping occurs due to friction, which eventually stops the system.

Characteristics of Simple Harmonic Motion

• Defined as periodic motion due to a restoring force (back to equilibrium) that is proportional to the displacement of the mass:

  • Equation:

    • Hooke's Law: ( F_{elastic} = -kx )

    • Where:

      • ( F_{elastic} ) = Spring force.

      • ( k ) = Spring constant (units: N/m).

      • ( x ) = Displacement from equilibrium.

  • The negative sign indicates force direction is opposite the displacement direction.

  • A larger spring constant ( k ) indicates a stiffer spring requiring more force to stretch or compress.

Energy in Springs

• A stretched or compressed spring stores energy:

  • Elastic potential energy equation: ( E_{elastic} = \frac{1}{2} kx^2 )

Simple Pendulum

• A simple pendulum also exhibits simple harmonic motion for small angles (<15°).

• The restoring force is a component of the bob’s weight, given by:

  • ( F_g = mg )

  • It’s greatest at large angles and zero at equilibrium.

• Gravitational potential energy increases as the pendulum's displacement increases.

Section Review (Page 445)

• Questions: 1-4.