Question

A small box with mass 0.7 kg  is attached to a spring (k=300 N/m ) and oscillates left and right. At a particular moment, the box is 20 cm to the right of its equilibrium position moving left with a speed of 2 m/s . What is the maximum distance to the right of its equilibrium position the box will reach? What is the maximum speed the box will have? What is the period of the box's oscillations?

Answer 1

A)

Using conservation of energy

0.5 kA^2 = 0.5 m v^2 + 0.5 k x^2

300* A^2 = 0.7* 2^2 + 350* 0.2^2

A = 0.2366 m

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B)

Angular frequency

w^2 = k/m = 300 / 0.7

w = 20.7 rad/s

Max velocity

v = Aw = 0.2366 x 20.7 = 4.898m/s

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C)

T = 2 pi / w = 2 pi/20.7 = 0.303 sec