Constrained Curvilinear Motion Acceleration

There is a drone that is surveying the park. The drone turns on and flies vertically upward to a height \(h\). Afterwards, the drone flies around in a pre-programmed path, while remaining at a constant height.
The path of the drone is governed by the following equations:
\(\theta(t) = 2\pi sin^3({{params.M1}}t + \frac{\pi}{2})\)
\(r(t) = {{params.N}} cos^4({{params.M2}}t + \frac{\pi}{2})\)
The origin point of this coordinate system is at the location where the drone starts the path as indicated on the figure.
Treat the drone as a particle which is constrained in the plane parallel to the ground at the height \(h\).

Part 1

What is the magnitude of the acceleration of the drone at time \(t = {{params.t}} \ \rm{s}\)?

Answer Section

Please enter in a numeric value in \(\rm{m/s^2}\).

Attribution

Problem is licensed under the CC-BY-NC-SA 4.0 license.