Question

Which of these forces could result in simple harmonic motion? The positive values of f(x) correspond to the forces acting in the positive x direction.

1) Gravitational force
2) Frictional force
3) Spring force
4) Magnetic force

Answer 1

The spring force, as described by Hooke's law, and the gravitational force in the case of a simple pendulum, are forces that can result in simple harmonic motion.

Step-by-step explanation:

The forces that could result in simple harmonic motion (SHM) are those that can provide a linear restoring force that is directly proportional to the displacement from an equilibrium position and acts in the opposite direction of that displacement. Among the choices given, the spring force described by Hooke's law, F = -kx, where F is the restoring force, k is the force constant, and x is the displacement from equilibrium, clearly satisfies this condition and can result in SHM. A gravitational force can also lead to SHM in the specific case of a simple pendulum with small amplitude, as Earth's gravity provides a restoring force that is proportional to the sine of the displacement angle, which for small angles can be approximated as directly proportional to the displacement itself.

However, the frictional force and magnetic force do not generally produce SHM as they do not tend to be proportional to displacement in a simple linear fashion and often include effects that are not conservative, such as energy dissipation in the case of friction.