A mass of 1 kg attached to a spring with a spring constant of 100. N/m oscillates horizontally on a smooth frictionless table with an amplitude of 0.5 m. When the mass is 0.25 m away from equilibrium, determine:
a) its total mechanical energy;
b) the system's potential energy and the mass's kinetic energy;
c) the mass's kinetic energy when it is at the equilibrium point.
d) Suppose there was friction between the mass and the table so that the amplitude was cut in half after some time. By what factor has the mass's maximum kinetic energy changed?
e) By what factor has the maximum potential energy changed?
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