3.21 A balloon carrying a first-order thermometer with a 15-s time constant rises through the atmosphere at 6 m/s. Assume temperature varies with altitude at 0.15°C/30m. The balloon radios temperature and altitude readings back to the ground. At 3000 m the balloon says the temperature is 0°C. What is the true altitude at which 0°C occurs? 3.22 A first-order instrument must measure signals with frequency content up to 100 Hz with an amplitude inaccuracy of 5 percent. What is the maximum allowable time constant? What will be the phase shift at 50 and 100 Hz? 3.23 For the spring scale of Fig. 3.50, discuss the trade-off between sensitivity and speed of response resulting from changes in K.. 3.25 Find the transfer function of a spring scale (Fig. 3.50) whose mass is negligible. Show that the steady-state time lag for a ramp input is the same whether mass is zero or not.