Question

A mass of 0.55kg is oscillating on the end of a vertical spring. What is the the displacement of the mass when it's upward acceleration is 11.90m/s?k=140N/m

Answer 1

Answer on Question #64120, Physics / Mechanics | Relativity

A mass of $0.55\,\mathrm{kg}$ is oscillating on the end of a vertical spring. What is the displacement of the mass when it's upward acceleration is $11.90\,\mathrm{m/s^2}$? $k = 140\,\mathrm{N/m}$.

Solution:

Mechanical model: mass m on a spring characterized by a spring constant k. Elastic restoring force $F = -kx$ is balanced according to Newton's second law

$$F = m a$$ $$m \ddot{x} = - k x$$

From equation of motion we have,

$$x = - \frac{m a}{k} = - \frac{(0.55)(11.90)}{140} = -0.047\,\mathrm{m}$$

Answer: $0.047\,\mathrm{m}$

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