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Concept · Mechanics
Simple harmonic motion & mechanical waves
SHM restoring force F=-kx and a opposite to x, period of mass-spring/pendulum T=2·π·√L/g, displacement/velocity/acceleration sign relations on graphs; mechanical waves transverse/longitudinal, v=f·λ, frequency set by source (unchanged across media)
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Named traps
15 ways this goes wrong.
Each is a named misconception the questions are built to catch. Open one for the move that tempts, and the fix.
- Acceleration not opposite displacementTakes acceleration in the same direction as displacement, missing that a=-(k/m)x always opposes x.→
- Amplitude affects speedAssumes a larger-amplitude wave travels faster in the same medium.→
- Frequency changes across mediaBelieves a wave's frequency changes when it enters a new medium, where frequency is fixed by the source.→
- Max acceleration at equilibriumPlaces maximum acceleration at the center rather than at maximum displacement.→
- Max speed at the extremesPlaces maximum speed at the amplitude extremes instead of at the equilibrium position.→
- Medium particles travel with waveBelieves the medium's particles move along with the wave rather than oscillating about fixed positions.→
- Pendulum period depends on massThinks the simple pendulum's period depends on the bob mass rather than only on L and g.→
- Restoring force sign wrongWrites F=+kx (away from equilibrium) instead of the restoring F=-kx directed toward equilibrium.→
- SHM period depends on amplitudeBelieves a larger amplitude lengthens the period of an ideal SHM oscillator.→
- Spring period k/m invertedUses T proportional to √k/m instead of √m/k, inverting the mass and stiffness roles.→
- Total SHM energy oscillatesBelieves total mechanical energy varies through the cycle, rather than KE and PE interchanging at constant total.→
- Transverse/longitudinal swappedClassifies sound as transverse or a wave on a string as longitudinal, swapping the oscillation-direction relationship.→
- Velocity and acceleration same signAssumes velocity and acceleration always share a sign in SHM, ignoring that they oppose while the body moves back toward equilibrium.→
- Wavelength read off time graphReads wavelength from a displacement-time graph (which shows period) or period from a displacement-distance graph.→
- v=f·λ misusedRearranges v=f·λ incorrectly, e.g. λ=v·f, or treats frequency as inversely proportional to speed.→
Key formulas
No formula sheet is matched to this concept yet. Work it from first principles, and watch the traps.
Shaky underneath?
If the concept underneath still feels loose, patch it here before coming back to CSCA questions.
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