Answer to Question #160907 in Classical Mechanics for Eva

Question

An object of mass 0.40kg, hanging from a spring with a spring constant of 8.0N/m, is set into an up-and down simple harmonic motion. What is the magnitude of the acceleration of the object when it is at its maximum displacement of 0.10m?

Answer 1

When the object is at its maximum displacement, the magnitude of the force exerted on it by the spring can be written as follows:

$$F=kx_{max}=8.0\ \dfrac{m}{s^2}\cdot0.1\ m=0.8\ N.$$

Finally, we can find the acceleration of the object from the Newton's Second Law of Motion:

$$a=\dfrac{F}{m}=\dfrac{0.8\ N}{0.4\ kg}=2\ \dfrac{m}{s^2}.$$