Question

problem 8:
a 2 kg raven oscillates on a tree branch with an amplitude of 8 cm and a period. assuming that the branch acts like a spring with a spring constant of 15 n/m, find the maximum speed the raven is bobbing on the branch using the conservation of energy. finally, find the maximum force on the raven by the branch.

Explanation:

Step1: Find the maximum speed

The conservation of energy gives \(E = \frac{1}{2}kA^{2}=\frac{1}{2}mv_{max}^{2}\).
We can solve for \(v_{max}\):

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Step2: Find the maximum force

The force in a spring is \(F=-kx\). The maximum force occurs when \(x = A\).

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Answer:

The maximum speed is approximately \(0.22\ m/s\) and the maximum force is \(1.2\ N\).