Period Scaling, Clocks, and Measurement
Oscillator periods scale as T proportional to sqrt(inertia/restoring coefficient); for a simple pendulum T proportional to sqrt(l/g), enabling clock-rate and graph analysis.
Why this shows up in the exam
Pendulum clocks at altitude or temperature · Experimental L versus T squared plots · Mass, length, stiffness, or planet scaling
Learn the idea
Period ratios expose how length, gravity, mass, stiffness, and thermal expansion change an oscillator. Most comparison questions become simple after identifying what changed and taking a ratio, avoiding repeated calculation of constants.
🧠 Memory hook: Period is the square root of inertia over restoring strength.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- T2/T1 = sqrt((I2/K2)/(I1/K1)) — general period ratio from inertia and restoring coefficient
- Delta T/T approximately equals 0.5 Delta l/l - 0.5 Delta g/g — small fractional change for a pendulum
- L = g T²/(4 pi²) — linear L versus T squared experimental relation
How to approach it
- 1Write the governing proportionality
- 2List fixed and changed quantities
- 3Form the ratio and interpret whether the clock gains or loses
Common slip-ups that cost marks
- •Reversing a square-root ratio
- •Treating clock gain as period gain
- •Changing mass in an ideal simple-pendulum formula
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A mass of 1 kg is attached to a spring of force constant 100 N/m. Find the angular frequency of small oscillations.
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