0
$\begingroup$

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.

$\endgroup$
1
  • $\begingroup$ What force are you asking about? The tension in the string? The restoring force? $\endgroup$ Nov 27, 2020 at 22:22

1 Answer 1

1
$\begingroup$

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.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.