PX155 - E15 - the compound pendulum

1

torque about $P :$

τ = - M g d \sin θ

τ = I_{p} \ddot{θ}

so,

- M g d \sin θ = I_{p} \ddot{θ}

I_{P} = I_{c m} + M d^{2}

for small $θ : \sin θ \approx θ$

- M g d θ \approx (I_{c m} + M d^{2}) \ddot{θ}

\ddot{θ} \approx \frac{- M g d}{I_{c m} + M d^{2}} θ

SHM with $ω^{2} = \frac{M g d}{I_{c m} + M d^{2}}$ , period $= \frac{2 π}{ω}$
to measure period - calculate $I_{c m}$ from experiment

2

a circular disc, radius $20 c m$ , is separated from a point $50 m$ from its centre. what is the oscillation period as a compound pendulum?
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