Question

CCH 14 Hw Problem 14.62 )16 of 18 Review 1 Constants 1 Periodic Table Part A The ultrasonic transducer used in a medical utrasound imaging SHM at 1.0 MHǐ byaneloctromagnetic col. The maximum nestoring fonce that can be applied to the disk without breaking disk? is 32,000 N, What is the maximum oscilation amplitude thet won't rupture the Express your answer with the appropriate units A- Value Units Submit Request Answer Part B What the dsk's maximum speed ฮ! this amplade? Express your answer with the approprlate units Value Units Submt Request Answer

Answer 1

(a) Since the displacement of the oscillator obeys the expression x(t) = A cos (ωt + δ),
then the acceleration is a = ¨x = −ω
2A cos (ωt + δ), and so the maximum acceleration
occurs when the cosine is -1. Thus, amax = Aω2
. The force associated with
this acceleration is F = ma, and so the maximum amplitude is
A =Fmω2 = F=4π^2mf^2
where f is the ordinary frequency. Plugging in the numbers gives
A =F4π^2mf^2

= 32000/(4π^2 × 10^−4 × (10^6)^2

= 8.11*10^−6 meters, MU*meters

(b) The maximum speed is found in the same way as the acceleration and gives
vmax = Aω = 2πfA, and so
vmax = 2πfA = 2π × 10^6 × 8.11*10^−6 ≈ 50.93 m/s.

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