Hooke's Law and Mass-Spring Motion

1. Robert Hooke

• English scientist (1635–1703).

• Studied elasticity: how objects stretch or compress when forces are applied.

• Developed Hooke’s Law describing how springs behave.

Displacement

Distance from equilibrium position.

• Positive = above equilibrium

• Negative = below equilibrium

Motion of Mass on a Spring

At Equilibrium

• displacement = 0

• velocity = maximum

• acceleration = 0

• net force = 0

At Maximum Stretch or Compression

• displacement = maximum

• velocity = 0

• acceleration = maximum

• restoring force = maximum

The mass stops momentarily and changes direction.

Velocity in SHM

• Velocity = 0 at maximum displacement.

• Velocity = maximum at equilibrium.

Acceleration in SHM

• Acceleration = 0 at equilibrium.

• Acceleration = maximum at maximum displacement.

Acceleration always points toward equilibrium.