Key relationship
Us = ½kx²; Ug = mgh; x(t) = −x₀ cos(√(k/m)t); K + Us = ½kx₀².
Physics · Class 11
Spring and potential energy
A spring stores energy as work is done against its restoring force. Because the force increases with deformation, spring energy is ½kx², not kx². Released on a frictionless platform, this energy alternates between elastic potential and kinetic forms. A raised platform adds constant gravitational potential mgh relative to the ground.
Open the interactive experiment →Compression stores energy quadratically.
சுருளின் நிலை ஆற்றல் ½kx². உராய்வு இல்லாமல் அது இயக்க ஆற்றலாகவும் மீண்டும் நிலை ஆற்றலாகவும் மாறும். ஈர்ப்பு நிலை ஆற்றல் தேர்ந்தெடுத்த அடிப்படையைச் சார்ந்தது.
Key notes, relationships and model limits
Remember
A spring stores energy as work is done against its restoring force. Because the force increases with deformation, spring energy is ½kx², not kx². Released on a frictionless platform, this energy alternates between elastic potential and kinetic forms. A raised platform adds constant gravitational potential mgh relative to the ground.
Common trap
Doubling compression quadruples stored spring energy; changing the gravity zero does not change the motion.
Model limits
Horizontal ideal massless Hooke-law spring on a platform of constant height; no friction or damping. Gravity potential depends on the chosen zero; the height remains constant during oscillation.
What you will learn
Calculate spring and gravitational potential energy and recognize dependence on deformation and reference level.
Try the experiment
Compare normal and double compression, then play. Raise the platform to see a constant added energy baseline.
Think of it this way
Compressing a toy spring stores the work that later launches or moves its load.
Worked example
For k = 40 N/m and x = 0.5 m, Us = 5 J. At x = 1 m it is 20 J. A 2 kg mass 2 m above ground additionally has Ug = 39.24 J.
Why this matters
Potential energy describes an interaction and a chosen reference, not an absolute property of an isolated object.
Before you start
Vector components · velocity · SI units
Check your understanding
If spring compression doubles while k stays fixed, stored energy becomes…
- Twice as large
- Four times as large
- Unchanged
Read the explanation
Us = ½kx² is proportional to the square of compression.
Course connection: CBSE XI Chapter 5; NEET/Main Unit 4; JEE Advanced Mechanics. Apply each exam’s stated assumptions.