Pendulum in an Accelerating Lift
Apply horizontal and vertical acceleration together. Observe how effective gravity changes the pendulum's equilibrium direction and period.
Effective gravity, geff9.81 m/s²
Equilibrium tilt0.0°
Period, T2.01 s
Current angle from vertical+10.0°
Lift acceleration
Positive = lift accelerates right. Negative = lift accelerates left.
Positive = upward acceleration. Negative = downward acceleration.
Measured around the tilted equilibrium direction.
No lift acceleration
Effective gravity is ordinary gravity, so the equilibrium string is vertical.
Sign convention: +x is right and +y is upward. In the accelerating lift,
the bob feels a pseudo-acceleration opposite to the lift acceleration.
Upward accelerationgeff increases → period decreases.
Downward accelerationgeff decreases → period increases.
Rightward accelerationpendulum equilibrium tilts left.
Leftward accelerationpendulum equilibrium tilts right.
geff = g − alift
geff = √[aₓ² + (g + aᵧ)²], T ≈ 2π√(L/geff)
geff = √[aₓ² + (g + aᵧ)²], T ≈ 2π√(L/geff)
Inside the accelerating lift
lift acceleration
gravity
effective gravity
oscillation about equilibrium