Question

You are to build the oscillation transfer device shown in Fig. 15-25. It consists of two spring–block systems hanging from a flexible rod. When the spring of system 1 is stretched and then released, the resulting SHM of system 1 at frequency f1 oscillates the rod. The rod then exerts a driving force on system 2, at the same frequency f1. You can choose from four springs with spring constants k of 1600, 1500, 1400, and 1200 N/m, and four blocks with masses m of 800, 500, 400, and200 kg. Mentally determine which spring should go with which block in each of the two systems to maximize the amplitude of oscillations in system 2.

a)

system 1: 1600 N/m with 800 kg
system 2: 1200 N/m with 200 kg

b)

system 1: 1600 N/m with 200 kg

system 2: 1200 N/m with 800 kg

c)

system 1: 1200 N/m with 400 kg

system 2: 1500 N/m with 500 kg

d)

system 1: 1500 N/m with 500 kg

system 2: 1200 N/m with 400 kg

which a or b or c or d is the correct answer and why?

Answer 1

The answer is (d).

It has to be (c) or (d) because those two systems match angular frequencyω =√(k/m). The first two systems, (a) and (b), havedifferentω for the two systems.

Between (c) and (d), consider that total energy is (1/2)kA² so between two systems with identical energy, the one with the lower springconstant k will have higher amplitude. That makes (d) the choice.