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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 potential energy (U) of the toy when the spring is compressed 4.4 cm from its equilibrium position? *I found the KE, but need help on PE*

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MathPhys

Answer:

0.14 J

Explanation:

The maximum velocity is the amplitude times the angular frequency.

vmax = Aω

ω = vmax / A

ω = (3.2 m/s) / (0.06 m)

ω = 53.3 rad/s

For a spring-mass system:

ω = √(k / m)

ω² = k / m

k = ω²m

k = (53.3 rad/s)² (0.050 kg)

k = 142 N/m

The elastic potential energy is:

EE = ½ kx²

EE = ½ (142 N/m) (0.044 m)²

EE = 0.14 J

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