The wind blowing on a spiders web initiates simple harmonic motion of the spider

Question

The wind blowing on a spiders web initiates simple harmonic motion of the spider in the center of web. If the mass of the spider is 0.20 grams. and you measure the maximum horizontal displacement as 1.8 cm, and the spider makes 15 oscillation in ten seconds.

(a) What is the amplitude of the oscillation of the spider?  

(b) What is the frequency of the spider's oscillation?

(c) What is the period of the oscillation?

(d) Assuming the web can be considered to be like a spring, what would be the spring constant for the spider of mass 0.20 grams oscillating at a frequency found in part (b)?

(e) What is the maximum Potential energy?

(f) What was the spider's maximum velocity?

Explanation / Answer

a)
Amplitude = maximum horizontal displacement
= 1.8 cm

b)
15 oscillations in 10 s
so,
frequency, f = 15/10 = 1.5 Hz

c)
Period, T = 1/f = 1/1.5 = 2/3 s

d)
m = 0.20 g = 2*10^-4 Kg
use:
f = 1/2pi * sqrt (k/m)
1.5= 1/2pi * sqrt(k/( 2*10^-4))

k/( 2*10^-4) = 88.83
k = 0.018 N/m
Answer: 0.018 N/m

I am allowed to answer only 4 parts at a time

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