\(a)\\T=\dfrac{2\pi}{\omega}=\dfrac{2\pi}{\pi}=2(s)\\f=\dfrac{1}{T}=\dfrac{1}{2}(Hz)\\b)\\t=2\Rightarrow \begin{cases} x=5\cos\left(2\pi +\dfrac{\pi}{6}\right)=\dfrac{5\sqrt{3}}{2}(cm)\\\omega t+\varphi=2\pi +\dfrac{\pi}{6}(rad)\end{cases}\\c)\\v=A\omega \cos\left(\omega t+\varphi+\dfrac{\pi}{2}\right)\\=5\pi\cos\left(\pi t+\dfrac{\pi}{6}+\dfrac{\pi}{2}\right)\\=5\pi\cos\left(\pi t+\dfrac{2\pi}{3}\right)\\a=-A\omega^2\cos\left(\pi t+\varphi \right)\\\Rightarrow a=-5\pi^2\cos\left(\pi t+\dfrac{\pi}{6}\right)\\=5\pi^2\cos\left(\pi t-\dfrac{5\pi}{6}\right)\\d)\\v_{max}=A\omega =5\pi(cm/s)\\a_{max}=A\omega^2=5\pi^2(cm/s^2)\\e)\\t=1,25(s)\Rightarrow \begin{cases}v=5\pi\cos\left(\pi .1,25+\dfrac{2\pi}{3}\right)=\dfrac{5\pi(\sqrt{6}+\sqrt{2})}{4}\approx 15,2(cm/s)\\a=5\pi^2\cos\left(\pi .1,25-\dfrac{5\pi}{6}\right)=\dfrac{5\pi^2(\sqrt{6}-\sqrt{2})}{4}\approx 13(cm/s)\end{cases}\)\(\\f)\\|v|=\omega\sqrt{A^2-x^2}=\pi\sqrt{5^2-\left(\dfrac{5\sqrt{2}}{2}\right)^2}=\dfrac{5\pi\sqrt{2}}{2}\approx 11,1(cm/s)\\g)\\a=-\omega^2x=-3\pi^2(cm/s^2)\\h)\\(A\omega)^2=v^2+\dfrac{a^2}{\omega^2}\\\Rightarrow (5\pi)^2=v^2+\dfrac{25^2}{\pi^2}\\\Rightarrow v\approx\pm 13,54(cm/s)\\i)\\(A\omega)^2=v^2+\dfrac{a^2}{\omega^2}\\\Rightarrow (5\pi)^2=(2,5\pi)^2+\dfrac{a^2}{\pi^2}\\\Rightarrow a=\pm\dfrac{5\pi^2\sqrt{3}}{2}\approx\pm42,7(cm/s^2)\\k)\\t=8s=4T\\\Rightarrow S=4.4A=80(cm)\)