5. (II) A small fly of mass 0.22g is caught in a spider s web. The web oscillates predominantly with a frequency of 4.0 Hz. (a) What is the value of the effective spring stiffness con- stant k for the web? (b)At what frequency would you expect the web to oscillate if an insect of mass 0.44 g were trapped?

Here's how to solve this problem, broken down into parts (a) and (b):**(a) Finding the spring stiffness constant (k)**The oscillation of the spider web can be modeled as a simple harmonic oscillator. The frequency (f) of a simple harmonic oscillator is related to the mass (m) and the spring constant (k) by the following equation:f = 1/(2π) * √(k/m)We are given:* f = 4.0 Hz* m = 0.22 g = 0.00022 kg (Remember to convert grams to kilograms!)We need to solve for k. Let's rearrange the equation:1. Square both sides: f² = (1/(4π²)) * (k/m)2. Multiply both sides by 4π²m: k = 4π²m f²Now, substitute the known values:k = 4π² * 0.00022 kg * (4.0 Hz)² k ≈ 0.14 N/mTherefore, the effective spring stiffness constant for the web is approximately 0.14 N/m.**(b) Finding the oscillation frequency with a different mass**Now, we have a new mass (m₂ = 0.44 g = 0.00044 kg) and we want to find the new frequency (f₂). We can use the same equation as before, but this time we'll solve for f₂:f₂ = 1/(2π) * √(k/m₂)We already found k in part (a). Substitute the values:f₂ = 1/(2π) * √(0.14 N/m / 0.00044 kg)f₂ ≈ 2.8 HzTherefore, if an insect of mass 0.44 g were trapped, we would expect the web to oscillate at a frequency of approximately 2.8 Hz. Note that this assumes the spring constant of the web remains the same. In reality, the web's stiffness might change slightly depending on how the insect is caught.