A 195-g object is attached to a spring that has a force constant of 71.5 N/m. Th

Question

A 195-g object is attached to a spring that has a force constant of 71.5 N/m. The object is pulled 9.25 cm to the right of equilibrium and released from rest to slide on a horizontal, frictionless table. Calculate the maximum speed of the object. (I've got the first answer of 1.8m/s, however I am having trouble with the second part)

Find the locations of the object when its velocity is one-third of the maximum speed. Treat the equilibrium position as zero, positions to the right as positive, and positions to the left as negative.

Explanation / Answer

Here,

let the position is x

k = 71.5 N/m

mass , m = 0.195 Kg

amplitude , A = 9.25 cm = 0.0925 m

Using conservation of energy

0.5 * k * x^2 + 0.5 * m * v^2 = 0.5 * k * A^2

71.5 * x^2 + 0.195 * (1.8/3)^2 = 0.5 * 71.5 * 0.0925^2

solving for x

x = -0.0574 m, 0.0574 m

the positions are 5.74 cm , - 5.74 cm

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