Pendulum in Effective Gravity and Fluids
For small pendulum motion in a uniformly accelerating frame, T = 2 pi sqrt(l/g_eff), where g_eff is the magnitude of g minus frame acceleration; buoyancy modifies the restoring weight separately.
Why this shows up in the exam
Pendulum in a lift or accelerating vehicle · Pendulum on an incline-descending support · Immersed pendulum and apparent-weight changes
Learn the idea
Acceleration of the support or buoyancy replaces ordinary gravity by an appropriate effective restoring field. Inside an accelerating frame the bob responds to the vector combination of gravity and the frame's inertial field; immersion reduces its effective weight.
🧠 Memory hook: Find the effective down direction before using the pendulum formula.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- g_eff_vector = g_vector - a_frame — effective gravity in a translating noninertial frame
- T = 2 pi sqrt(l/g_eff) — period about the effective vertical
- g_b = g(1-rho_fluid/rho_bob) — effective restoring acceleration for a fully immersed dense bob
How to approach it
- 1Draw gravity and frame acceleration vectors
- 2Find the equilibrium direction and magnitude
- 3Then apply the small-angle formula or buoyant correction
Common slip-ups that cost marks
- •Adding acceleration as scalars when directions differ
- •Using zero period in free fall instead of no stable pendulum oscillation
- •Ignoring buoyancy while keeping ordinary weight
🌟 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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