Question

Consider a 0.04kg mass on a level, frictionless surface and connected to a 180N/m spring constant. Pull the mass to x = 0.1 meter and release. Determine the KE when x = 0.4 meter

Answer #1

As the maximum displacemet of the mass is 0.1m so we cannot determine kinetic energy at x = 0.4m as it is more than the maximum displacemet. So assuming x = 0.04m.

Let,

a = 0.1 m is the amplitude of oscillation

K = 180 N/m is the spring constant.

x = 0.04 m is the displacement

Kinetic energy of the oscillating mass = change in potential energy of the oscillating mass

Kinetic energy = (1/2)Ka^{2} - (1/2)Kx^{2}

Kinetic energy = (1/2)×180×(0.1)^{2} -
(1/2)×180×(0.04)^{2}

Kinetic energy = 0.9 - 0.144

Kinetic energy = 0.756 J

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