A 1.00 kg mass is connected to a spring with a spring constant of 9.00 N/m.If the initial velocity is 4.00 cm/s and the initial displacement is 0.00 cm,then what is the maximum displacement of the simple harmonic motion?
A) 2.67 cm
B) 2.33 cm
C) 2.05 cm
D) 1.67 cm
E) 1.33 cm

Question

Quizplus · Accepted Answer

The maximum displacement (amplitude) can be found using the formula for kinetic energy and potential energy in simple harmonic motion. The initial kinetic energy is converted to potential energy at maximum displacement: (1/2)mv^2 = (1/2)kA^2. Solving for A gives A = v * sqrt(m/k) = 4 cm/s * sqrt(1 kg / 9 N/m) = 1.33 cm.

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