Question

1. (6 pts.) A spring has a spring constant of 250 N / m and has a tied mass of 100 grams. The spring is stretched by 40 cm. Determine: a) the period of oscillation. b) position for the time of 0.045 seconds.

2. (6 pts.) For the spring of Problem 1, calculate a) the mechanical energy. b) the two positions where the mass has a speed of 5.0 m / s

Answer 1

Angular frequency of syatem

w^2 = k/m

w^2 = 250 / 0.1

w = 50 rad/s

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a)

w = 2"pi / T

50 = 2 pi / T

T = 0.1256 s

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b)

Instantaneous position

x = A cos ( wt)

x = 0.4 cos ( 50 t)

At t = 0.045 s

x = - 0.251 m

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c)

Mechanical energy

E= 0. 5 k x^2 = 20 J

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d)

Using energy conservation

0.5 k x^2 = 0.5 k a^2 - 0.5 m v^2

250 x^2 = 250* 0.4^2 - 0.1* 5^2

x = ± 0.387 m

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