What is the maximum kinetic energy of a 2.00-kg mass moving with simple harmonic motion with an amplitude 5.00 cm and period 0.300 s?
A)1.10 J
B)0.444 J
C)0.222 J
D)0.174 J
E)0.0278 J

Question

Quizplus · Accepted Answer

The maximum kinetic energy of a mass in simple harmonic motion is given by:$$K_{max}=\frac{1}{2}kA^2$$where k is the spring constant and A is the amplitude. The spring constant is given by:$$k=\frac{4\pi^2m}{T^2}$$where m is the mass and T is the period. Substituting these expressions into the equation for the maximum kinetic energy, we get:$$K_{max}=\frac{1}{2}\left(\frac{4\pi^2m}{T^2}ight)A^2$$Plugging in the given values, we get:$$K_{max}=\frac{1}{2}\left(\frac{4\pi^2(2.00	ext{ kg})}{(0.300	ext{ s})^2}ight)(0.0500	ext{ m})^2=1.10	ext{ J}$$

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