A mass m = 8,kg is attached to a spring as sh | vedclass

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(B) The system consists of a mass $m$ attached to a spring via a pulley. When the mass is released from the position where the spring is unstretched,t

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$2$

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(B) The system consists of a mass $m$ attached to a spring via a pulley. When the mass is released from the position where the spring is unstretched,the equilibrium position is reached when the spring force equals the gravitational force.At equilibrium,$k x_{eq} = mg$,so the equilibrium extension is $x_{eq} = \frac{mg}{k} = \frac{8 	imes 10}{200} = 0.4\,m$.The amplitude of oscillation $A$ is equal to the initial extension from the equilibrium position,which is $A = x_{eq} = 0.4\,m$.The angular frequency of the oscillation is $\omega = \sqrt{\frac{k}{m}} = \sqrt{\frac{200}{8}} = \sqrt{25} = 5\,rad/s$.The maximum velocity $v_{max}$ is given by $v_{max} = \omega A$.Substituting the values,$v_{max} = 5 	imes 0.4 = 2\,m/s$.

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