# Force versus time and force versus angular displacement graph - simple pendulum

How to graph Force versus time and force versus angular displacement graph in simple harmonic motion of a pendulum system (Force= net force directed towards equilibrium) It seems to me that force versus displacement graph should be linear (for small angles), but I might be wrong.

• What force are you asking about? The tension in the string? The restoring force? Nov 27, 2020 at 22:22

Assuming you are considering the forces that act along the pendulum bob's path, then the following is true for small angles:

Force vs. angular displacement

The graph is a straight line: $$F=-mg \theta\tag{1}.$$

Force vs time

Recall the simple pendulum equation $$\theta(t)=\theta_0\cos(\omega t+\phi)\tag{2}$$ where $$\omega=\sqrt{g/L}$$. Now substitute (2) into (1) and get:

$$F=-mg \theta_0\cos(\omega t+\phi).$$

Therefore, the graph is a sinusoid.

I would also add that this only applies when considering point masses, i.e. for simple pendulums.