91影视

Mass of the boat \(m = 1500\,{\rm{kg}}\)

The amplitude \(A = \,\,{\rm{20}}\,{\rm{cm}}\)

Time period of boat \(T = 3.5\,{\rm{s}}\)

A motion known as a "simple harmonic motion," or SHM, is one in which the restoring force is directly proportional to the body's displacement from its mean position.

Displacement of SHM is expressed as,

\(\begin{aligned}{l}x = A\cos (\omega t + \varphi )\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,i.e\,\,\varphi = 0\\x = A\cos (\omega t)\,\end{aligned}\) 鈥�(i)

Where, \(x\) is the displacement, \(A\) is the displacement, \(\omega \) is the angular speed and \(t\) is the time

Using equation (i)

\(x = A\cos (\omega t)\,\)

Substitute \(x = \frac{A}{2}\) and \(\omega = \frac{{2\pi }}{T}\) in above equation

\(\begin{aligned}{c}\frac{A}{2} = A\cos (\frac{{2\pi }}{T}t)\,\\\cos (\frac{{2\pi }}{T}t)\, = \frac{1}{2}\\\frac{{2\pi }}{T}t = {\cos ^{ - 1}}\left( {\frac{1}{2}} \right)\\\frac{{2\pi }}{T}t = \frac{\pi }{3}\\t = \frac{T}{6}\end{aligned}\)

So the time taken for full up and down motion is given by,

\(\begin{aligned}{c}2t = \frac{T}{3}\\ = \frac{{3.5\,{\rm{s}}}}{3}\\ = 1.17\,{\rm{s}}\end{aligned}\)