Question

A. Suppose you were given a spring with spring constant 4.9 N/m. If you wanted to set up a situation with an object undergoing simple harmonic motion (assuming it moves along a smooth horizontal surface) with a period of 0.63 s, what should be the mass of the object you choose to attach to the end of the spring? Give your answer in g.

B. The intensity of a particular earthquake wave is measured to be 2.2MW/m² at a distance of 51.0 km from the source. What was the intensity when it passed a point only 1.0 km from the source?
Give your answer in giga Watts per square metre, where 1GW/m²=1,000MW/m²=1,000,000,000W/m². Assume the energy is radiated uniformly in all directions.

Answer 1

a)
Time period, T = 0.63 s
Angular velocity, = 2/T
= 2/0.63
= 9.973 rad/s

Using the formula, k = m²,
Where k is the spring constant and m is the mass to be attached.
m = k/²
= 4.9/(9.973)²
= 0.04926
= 49.26 g

b)
Consider the intensity at the source = I
Intensity at the radius R, I_R = 51 km = I/R²
Given that I_R = 2.2 MW/m²
I = I_R x R²
= 2.2 MW/m² x R²
Intensity at the radius r = 1 km, I_r = I/r²
= [2.2 x R²] / r²
= 2.2 x (51 x 10³) / (1 x 10³)]²                        [Cancelling ]
= 2.2 x 51²
= 5722.2 MW/m²
= 5.72 GW/m²