1. The New England Merchants Bank Building in Boston is 152 m high. On windy day

Question

1. The New England Merchants Bank Building in Boston is 152 m high. On windy days it sways with a frequency of 0.22 Hz , and the acceleration of the top of the building can reach 2.3 % of the free-fall acceleration, enough to cause discomfort for occupants.

What is the total distance, side to side, that the top of the building moves during such an oscillation?

2. A 50-cm-long spring is suspended from the ceiling. A 210 g mass is connected to the end and held at rest with the spring unstretched. The mass is released and falls, stretching the spring by28 cm before coming to rest at its lowest point. It then continues to oscillate vertically.

a. What is the spring constant?

b. What is the amplitude of the oscillation?

c. What is the frequency of the oscillation?

Explanation / Answer

Assuming the oscillation is shm ..

Acceleration .. a = (-) ² x
( = equivalent ang. vel. = 2.f) (x = displacement from equilibrium position)

x (max) = a(max) /²

x = (0.023 x 9.8m/s²) / (2.f)²

x(max) = 0.117m .. (7.70cm)

2.

change in GPE = change in U = U
0.21kg * 9.8m/s² * 0.28m = 0.576 J = ½kx² = ½ * k * (0.28m)²
k = 14.69 N/m spring constant
A = 14 cm amplitude
f = (1/2)(k/m) = (1/2)(14.69kg/s² / 0.21kg) = 1.33 Hz frequency

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