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To practice Problem-Solving Strategy: Simple Harmonic Motion II: Energy. A child's toy consists of a spherical object of mass 50 g attached to a spring. One end of the spring is fixed to the side of the baby's crib so that when the baby pulls on the toy and lets go, the object oscillates horizontally with a simple harmonic motion. The amplitude of the oscillation is 6 cm and the maximum velocity achieved by the toy is 3.2 m/s . What is the kinetic energy K of the toy when the spring is compressed 3.7 cm from its equilibrium position?

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Answer:

0.15864 J

Explanation:

m = Mass of toy = 50 g

A = Amplitude = 6 cm

x = Compression of spring = 3.7 cm

[tex]v_m[/tex] = Maximum velocity = 3.2 m/s

The kinetic energy of the system is given by

[tex]K=\frac{1}{2}m\left(\omega \sqrt{A^2-x^2}\right)^2\\\Rightarrow K=\frac{1}{2}m\left(\frac{v_m}{A} \sqrt{A^2-x^2}\right)^2[/tex]

[tex]K=\frac{1}{2}\times 0.05\left(\frac{3.2}{0.06}\times \sqrt{0.06^2-0.037^2}\right)^2\\\Rightarrow K=0.15864\ J[/tex]

The kinetic energy of the toy is 0.15864 J

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