## College Physics (4th Edition)

The oscillation frequency when no one is sitting on the horse is $2.5~Hz$
We can find the spring constant $k$: $kx = mg$ $k = \frac{mg}{x}$ $k = \frac{(24~kg)(9.80~m/s^2)}{0.28~m}$ $k = 840~N/m$ Let $m_c$ be the mass of the child. We can find the mass of the horse $m_h$: $\omega = 2\pi~f$ $\sqrt{\frac{k}{m_c+m_h}} = 2\pi~f$ $m_c+m_h = \frac{k}{(2\pi~f)^2}$ $m_h = \frac{k}{(2\pi~f)^2}-m_c$ $m_h = \frac{840~N/m}{(2\pi)^2(0.88~Hz)^2}-(24~kg)$ $m_h = 3.476~kg$ We can find the oscillation frequency when no one is sitting on the horse: $2\pi~f = \omega$ $f = \frac{\omega}{2\pi}$ $f = \frac{1}{2\pi}~\sqrt{\frac{k}{m_h}}$ $f = \frac{1}{2\pi}~\sqrt{\frac{840~N/m}{3.476~kg}}$ $f = 2.5~Hz$ The oscillation frequency when no one is sitting on the horse is $2.5~Hz$.