# A mass-spring system oscillates with an amplitude of 5.80 cm. If the spring constant is 275 N/m and the mass is 582 g,?

A mass-spring system oscillates with an amplitude of 5.80 cm. If the spring constant is 275 N/m and the mass is 582 g,

1. determine the mechanical energy of the system.

2. Determine the maximum speed of the object.

3. Determine the maximum acceleration.

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• Anonymous
7 months ago

1)

E = 1/2 k A^2

E = 0.5 * 275 * 0.058^2 = 0.46 J

2)

v = w A = sqrt(k/m) A

v = sqrt(275/0.582) * 0.058 = 1.26 m/s

3)

a = w^2 A = (k/m) A

a = (275/0.582) * 0.058 = 27.41 m/s^2

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• To solve this problem, I will assume the spring is moving horizontally. The following equation is used to calculate the mechanical energy.

ME = ½ * k * d^2 = ½ * 275 * 0.058^2 = 0.46255 J

2. Determine the maximum speed of the object.

The maximum speed occurs when all of the mechanical energy has been converted into kinetic energy.

KE = ½ * 0.582 * v^2 = 0.291 * v^2

0.291 * v^2 = 0.46255

v = √(0.46255 ÷ 0.291)

This is approximately 1.59 m/s.

3. Determine the maximum acceleration.

The maximum acceleration occurs when the spring is exerting the maximum force. The equation for the maximum force is shown below.

Maximum force = k * d

F = 275 * 0.058 = 15.95 N

15.95 = 0.582 * a

a = 15.95 ÷ 0.582

This is approximately 27.4 m/s^2. I hope this is helpful for you.

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