💡 Hooke's Law
F = -kx — The force exerted by a spring is proportional to its displacement from equilibrium. The negative sign indicates the force opposes the displacement (restoring force).
Spring Calculator
Configure spring parameters
Solve for:
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Spring Constant (k)
↔️
Displacement (x)
Spring Force
10.00 N
Elastic PE
0.50 J
Spring Constant
100 N/m
Displacement
0.10 m
📚 Try These Examples
Car Suspension
k=50000 N/m, x=5cm
Pen Spring
k=500 N/m, x=1cm
Mattress Spring
k=2000 N/m, x=3cm
Watch Spring
k=50 N/m, x=2mm
🌀 Spring Visualization
k = 100 N/m
x = 0.10 m
F = 10 N
📝 Spring Formulas
F = -kx
Hooke's Law
PE = ½kx²
Elastic Potential Energy
k = F/x
Spring Constant
T = 2π√(m/k)
Oscillation Period
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Step-by-Step Solution
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Understanding Hooke's Law and Springs
Hooke's Law describes the behavior of elastic materials like springs. When a spring is stretched or compressed from its natural length, it exerts a restoring force proportional to the displacement.
Key Concepts
- Spring Constant (k): Measures stiffness - higher k means stiffer spring
- Displacement (x): Distance from equilibrium position (can be + or -)
- Restoring Force: The negative sign means force opposes displacement
- Elastic Limit: Beyond this point, Hooke's Law no longer applies
Elastic Potential Energy
When a spring is deformed, it stores elastic potential energy: PE = ½kx². This energy can be converted to kinetic energy (like in a spring-loaded toy).
Real-World Applications
- Vehicle Suspension: Springs absorb bumps (k ≈ 20,000-100,000 N/m)
- Mattresses: Provide comfort and support (k ≈ 1,000-5,000 N/m)
- Mechanical Watches: Hairspring controls timing (k ≈ 10-100 N/m)
- Trampolines: Convert PE to KE for jumping