a mercury therommometer having time constant $1\mathrm{.}0$ min is placed in temp bath at $100\backslash$deg F and allowd to come to equilibrium with the bath at time t$=0,$ the temperature of the bath begins to vary sinusoidally about

its average temperature of $100$F with an amplitude of

$2$F$.$ If the frequency of oscillation is $10/-$

cycles$/$min$,$

plot the ultimate response of the thermometer reading

as a function of time. What is the phase lag?