1. Rewrite the sinusoidal response of a first-order system [Eq. (5.24)] in terms of a cosine wave…

1. Rewrite the sinusoidal response of a
first-order system [Eq. (5.24)] in terms of a cosine wave. Reexpress the
forcing function [Eq. (5.19)] as a cosine wave, and compute the phase
difference between input and output cosine waves.

2. The mercury thermometer of Prob. 5.6
is again allowed to come to equilibrium in the room air at 75F. Then it is
placed in the 400F oil bath for a length of time less than 1 set, and quickly
removed from the bath and reexposed to the 75F ambient conditions. It may
be estimated that the heat-transfer coefficient to the thermometer in air is
one-fifth that

1. Rewrite the sinusoidal response of a
first-order system [Eq. (5.24)] in terms of a cosine wave. Reexpress the
forcing function [Eq. (5.19)] as a cosine wave, and compute the phase
difference between input and output cosine waves.

2. The mercury thermometer of Prob. 5.6
is again allowed to come to equilibrium in the room air at 75F. Then it is
placed in the 400F oil bath for a length of time less than 1 set, and quickly
removed from the bath and reexposed to the 75F ambient conditions. It may
be estimated that the heat-transfer coefficient to the thermometer in air is
one-fifth that in the oil bath. If 10 set after the thermometer is removed from
the bath it reads 98F, estimate the length of time that the thermometer was in
the bath.

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