A block of mass is attached to the end of a spring (spring stiffness constant ).

Question

A block of mass is attached to the end of a spring (spring stiffness constant ). The mass is given an initial displacement from equilibrium, and an initial speed .Ignoring friction and the mass of the spring, use energy methods to find its maximum speed. Ignoring friction and the mass of the spring, use energy methods to find its maximum stretch from equilibrium, in terms of the given quantities.

Explanation / Answer

Let mass be 'm' Initially: KE = 0 PE = k(x^2)/2 (x is initial dispacement) Total Energy=KE+PE=k(x^2)/2 SINCE TOTAL ENERGY is a constant, by conservation laws of energy, FOr maximum speed, KE is maximum => PE=0 ie KE=k(x^2)/2 = mv^2/2 => v=x*sqrt(k/m) MAximum stretch is when PE=max ie stretch is max when extension is 'x' Hope my detailed explanation helps :)

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