ばねの力

The more you stretch, the harder it pulls

• Pull a spring a little and it tugs back gently; pull it twice as far and it tugs back twice as hard.
• Let go and it snaps toward its rest position every time.
• This tidy, proportional push-back is what makes springs so predictable.
• It is also the recipe for every oscillation in physics.

Hooke's law

• Hooke's law 胡克定律 describes an ideal spring:

• The force is proportional to how far the spring is stretched or squeezed.
• The minus sign says the force always points back toward equilibrium.

Stiffness and displacement

• The spring constant 弹簧劲度系数 $k$ measures stiffness -- a bigger $k$ is a harder spring.
• The displacement 位移 $x$ is measured from the spring's natural rest length.
• On a graph of force versus displacement, $k$ is simply the slope.

A restoring force

• Because it always points back to the middle, the spring force is a restoring force 回复力.
• Stretch right → it pulls left; compress left → it pushes right.
• That constant "return to center" is exactly what drives a mass on a spring to oscillate.

Combining springs

• Springs in parallel 并联 (side by side) act stiffer: $k_{eq} = k_1 + k_2$.
• Springs in series 串联 (end to end) act softer: $\dfrac{1}{k_{eq}} = \dfrac{1}{k_1} + \dfrac{1}{k_2}$.
• It is the exact opposite of how resistors combine.