Question

2. i. Define simple harmonic motion

iii. Show that a mass, m, hung on a spring of spring constant, k, when

Answer 1

In simple harmonic motion, the acceleration of the system, and therefore the net force, is proportional to the displacement and acts in the opposite direction of the displacement.

A good example of SHM is an object with mass m attached to a spring on a frictionless surface The object oscillates around the equilibrium position, and the net force on the object is equal to the force provided by the spring. This force obeys Hooke’s law.

$$a+\omega^2x=0\\x=A\cos{(\omega t+\phi)}$$

Where

$$\omega=\sqrt{\frac{k}{m}}$$