Two springs, one block
"Two springs, one block" is a free, interactive Class 11 Physics simulation for NEET and JEE, built on the NCERT section "Force law for SHM: F = −kx" in Oscillations. One block with springs in series, parallel, or one on each side; effective k and period update, and the springs' extensions are drawn. NEET has asked about this idea 2 times in 10 years of papers. JEE Main asked 29 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
From the lesson Force law for SHM: F = −kx in Oscillations. Change the values and watch what happens.
What it shows
NCERT §13.6
One block with springs in series, parallel, or one on each side; effective k and period update, and the springs' extensions are drawn.
Controls
3 to try
- Togglesingle / series / parallel / both sides
- Sliderk₁, k₂ 10–100 N/m
- Slidermass 0.5–4 kg
Try this
Arrange two 50 N/m springs so the 1 kg block's period is 0.63 s (k_eff = 100: parallel or both sides).
Common mistake
Using k for a block between two springs; adding k in series.
In NEET
10 years of papers
Asked 2 times in 10 years of NEET.
See the past questions: Newton's Laws of Motion, Simple Harmonic Motion, Oscillations (chapter)
In JEE Main
42 shifts analysed
29 questions from Oscillations across the 42 JEE Main shifts Lumi has analysed (2017–2026).
The idea behind it
NCERT §13.6
- Newton's second law with a = −ω²x gives the force on a particle of mass m in SHM: F = ma = −mω²x, written F = −kx with k = mω².
- So ω = √(k/m) and the period is T = 2π√(m/k). A stiffer spring makes it faster; a heavier block makes it slower.
- The force always points towards the mean position, which is why it is called the restoring force.
- SHM can be defined in either of two equivalent ways: by the displacement x(t) = A cos(ωt + φ), or by the force law F = −kx. Differentiating the first twice gives the second; integrating the second twice gives back the first.
- A body acted on by a force exactly proportional to x is a linear harmonic oscillator. If the force also contains small terms in x², x³ and so on, it is a non-linear oscillator.
- Test for SHM: the acceleration must be a negative constant times x. a = −(constant) × x is SHM; an acceleration proportional to +x, to x² or to x³ is not.
- Worked example: a block of mass m held between two identical springs of constant k fixed on either side. Displaced by x, one spring stretches and the other compresses by x, and both push it back, so F = −2kx and T = 2π√(m/2k).
- The period of SHM does not depend on the amplitude, the energy or the phase constant; it is set only by m and k.
Questions
5 answers
- What does the "Two springs, one block" simulation show?
- One block with springs in series, parallel, or one on each side; effective k and period update, and the springs' extensions are drawn.
- What mistake does the "Two springs, one block" simulation fix?
- A common mistake it clears up: using k for a block between two springs; adding k in series.
- Has NEET asked about this idea?
- Yes. NEET has asked about this idea 2 times in 10 years of papers.
- Does JEE Main ask questions from Oscillations?
- Yes. JEE Main asked 29 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
- Is this simulation free?
- Yes. It is free and runs in the browser on a phone or a laptop. It belongs to the lesson "Force law for SHM: F = −kx" in Oscillations (Class 11 Physics).
Embed this simulation
Free, with a link back
Teaching this idea? Put the simulation on your own page or LMS with this code.