Block on a spring: what sets the period?
"Block on a spring: what sets the period?" is a free, interactive Class 11 Physics simulation for NEET and JEE, built on the lesson "Force law for SHM: F = −kx" in Oscillations. Change the block's mass and the spring's stiffness. Watch the period, and see that the purple force arrow always points back to the dashed mean line. F = −kx gives ω = √(k/m) and T = 2π√(m/k). The pull of 10 cm never enters: the period is the same for any amplitude. The speed is largest at the mean line and zero at the ends, where the force is largest. 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.
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
3 answers
- What does the "Block on a spring: what sets the period?" simulation show?
- Change the block's mass and the spring's stiffness. Watch the period, and see that the purple force arrow always points back to the dashed mean line.
- 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).
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