State and explain whether the pendulum period is a proper time interval for observer T, observer G or both T and G.

Observer T measures the period of oscillations of the pendulum to be 0.850s. Calculate the period of oscillations according to observer G.

Observer T is standing in the middle of a train watched by observer G at the side of the track. Two lightning strikes hit the ends of
the train. The strikes are simultaneous according to observer T.

Light from the strikes reaches both observers.

(i) Explain why, according to observer G, light from the two strikes reaches observer T at the same time.

(ii) Using your answer to (i), explain why, according to observer G, end X of the train was hit by lightning first.

only T measures the proper time interval;
for T the pendulum is (a single clock) at rest/same point in space;
Do NOT simply allow that the pendulum is in the same frame as T.

\(\gamma  = \left( {\frac{1}{{\sqrt {1 - {{0.95}^2}} }} = } \right)3.20\);
\(T = \left( {\gamma {T_0} = 3.20 \times 0.85 = } \right)2.72{\rm{s}}\);

(i) the arrivals at T of the light from the two strikes occurs at the same point in space for T and are simultaneous for T;
so the arrivals of the light are simultaneous for all other observers as well;

or

T measures a zero proper time interval for the arrivals of the light;
so G measures a time interval equal to \(\gamma \)×0=0 also;

(ii) according to G, T is moving away from the light from the left strike and yet receives the light at the same time as the light from the right strike;
since the speed of light is the same for light from both strikes;
the left strike occurred first
No marks for just stating left strike is first. Given.