Answer to Question #218192 in Physics for ran li

Question

A 250-g object hangs from a spring that has a spring constant of 48.0 N/m and oscillates with an amplitude of 5.42 cm.

1.The magnitude of the objects acceleration when the displacement is 4.27 cm [down] is ___m/s². (Give your answer with the correct number of sig digs and do not include units).

2.Given that the object has an amplitude of 5.42cm, the maximum speed that the object is ___m/s. (Give your answer with the correct number of sig digs and do not include units).

3.A 78.5-kg man is about to complete a bungee jump. If the bungee cord has a spring constant of 150 N/m, the period of oscillation that he will experience is ___s. (Give your answer with the correct number of sig digs and do not include units)

4.If a 5.00-kg mass oscillates on a spring with a frequency of 0.667 Hz the spring constant is ___N/m (Give your answer with the correct number of sig digs and do not include units in your answer)

Answer 1

1)

$$a=\frac{k}{m}x\\a=\frac{48}{0.25}0.0542=10.4\frac{m}{s^2}\\$$

2)

$$v=\sqrt{\frac{48}{0.25}}0.0542=0.751\frac{m}{s}\\$$

3)

$$T=2\pi\sqrt{\frac{78.5}{150}}=4.55\ s$$

4)

$$\frac{1}{0.667}=2\pi\sqrt{\frac{5}{k}}\\k=87.8\frac{N}{m}$$