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A spring of spring constant k sits on a frictionless horizontal surface, one end of the...

A spring of spring constant k sits on a frictionless horizontal surface, one end of the spring is attached to a wall, the other end to a block of mass M, also resting on the frictionless surface. The system executes simple harmonic motion such that at a given point the mass is -1/6 of the amplitude moving away from equilibrium, and 0.5 seconds later it has 1/7 of the maximum speeds, moving towards equilibrium, having passed equilibrium once.

1) How much time passes between the instant when the mass has a speed that is ½ its maximum speed moving away from equilibrium to it having ½ the maximum speed moving towards equilibrium?

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