Answer
a 2.72 s.
b. 1.19 s.
Work Step by Step
a. The interval, measured on the ship, is the proper time $\Delta t_o$. The pendulum at rest there.
The value of $\gamma$ is $\frac{1}{\sqrt{1-u^{2}/c^{2}}}=1.51$.
The mission control person measures a dilated time interval of $\gamma \Delta t_o =\gamma (1.80s)=2.72s$.
b. If the dilated time interval were 1.80s, the proper time interval would be $\frac{1.80s}{\gamma}=1.19s$.
