An average adult elephant $(5000\,\text{kg})$ is strapped to a spring, which is then pulled $2\,\text{meters}$ away from its equilibrium position and released. The elephant starts oscillating back and forth with a period of $10$ seconds.

Question

An average adult elephant $(5000\,\text{kg})$ is strapped to a spring, which is then pulled $2\,\text{meters}$ away from its equilibrium position and released. The elephant starts oscillating back and forth with a period of $10$ seconds.(a) Determine the spring constant of the spring.
, (b) Write down the equation of motion (position equation) for the elephant on the spring.
, (c) Calculate how long it will take the elephant to travel from a displacement of $0.5\,\text{m}$ to a displacement of $1\,\text{m}$.
:

Rita · Accepted Answer

$k = 200\pi^2 \text{ N/m}$
$x(t) = 2\cos(\frac{\pi}{5}t)$
$\Delta t = \frac{5}{\pi}(\cos^{-1}(0.25)-\frac{\pi}{3}) \approx 0.43\;\text{s}$

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