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What is the difference between ideal and non-ideal springs?

Ideal springs have negligible mass and perfectly obey Hooke's Law. Non-ideal springs have mass and may not perfectly obey Hooke's Law.

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What is the difference between ideal and non-ideal springs?
Ideal springs have negligible mass and perfectly obey Hooke's Law. Non-ideal springs have mass and may not perfectly obey Hooke's Law.
Compare springs in series and springs in parallel regarding their stiffness.
Springs in series are more compliant (less stiff). Springs in parallel are stiffer.
How does displacement relate to force in springs arranged in series versus parallel?
In series, total displacement is the sum of individual displacements. In parallel, the total force is the sum of individual forces.
Define Hooke's Law.
The force a spring exerts is directly proportional to its displacement from equilibrium: $\vec{F}_{s}=-k \Delta \vec{x}$
What is the spring constant ($k$)?
A measure of a spring's stiffness; the higher the value, the stiffer the spring.
Define 'equilibrium position' in the context of a spring.
The position where the spring is neither stretched nor compressed, and the net force on it is zero.
What is an ideal spring?
A spring with negligible mass that exerts a force perfectly proportional to its displacement from equilibrium.
Define equivalent spring constant.
A single spring constant that represents the combined effect of multiple springs in a system.
What is a restoring force?
A force that acts to bring a system back to its equilibrium position.
What is the difference between displacement and length in spring problems?
Displacement (Δx) is the change in length from the equilibrium position, while length is the total length of the spring.
Compare a spring with a high spring constant to one with a low spring constant.
High k: Stiffer, requires more force for the same displacement. | Low k: Less stiff, requires less force for the same displacement.
Compare stretching a spring vs. compressing a spring.
Stretching: Positive Δx, spring pulls back. | Compressing: Negative Δx, spring pushes back.
Compare the spring force at maximum displacement vs. at equilibrium.
Maximum displacement: Spring force is maximum. | Equilibrium: Spring force is zero.
Compare the energy stored in a stretched spring vs. a compressed spring (same |Δx|).
Stretched: Stores potential energy. | Compressed: Stores potential energy. Both store the same amount of potential energy if |Δx| is the same.