Differential equation for motion of a pendulum

In summary, the conversation discusses creating a model of pendulum motion in Matlab with non-linear components and finding the best fit using a sinusoid with an envelope given by a parabola. The equations of motion are provided and the question is asked about changing the equation to find a solution that matches the sinusoid. The response suggests linearizing the equation by assuming a small angle of swing.
  • #1
fiso
1
0
Hello,

I'm trying to create a model of pendulum motion in Matlab to fit the curve we measured in class, and it has some non-linear components (friction). It looks like the best fit is a sinusoid with an envelope given by a parabola (see attached file).

The equations of motion are given by:
[itex]\ddot{\phi}(t) = -k_2\dot{\phi}(t)-k_3\sin(\phi(t))[/itex]

How this equation can be changed so that the solution of it is a searched sinusoid?

Thank you.

// edit: please move this to Differential Equations
 

Attachments

  • response.png
    response.png
    22.2 KB · Views: 470
Last edited:
Physics news on Phys.org
  • #2
The usual approach is to linearize, assuming the angle of the swing is small, so replace sin(φ(t)) by φ(t).
 

FAQ: Differential equation for motion of a pendulum

What is a differential equation for the motion of a pendulum?

A differential equation for the motion of a pendulum is a mathematical equation that describes the motion of a pendulum based on its position, velocity, and acceleration over time. It takes into account various factors such as the length of the pendulum, the force of gravity, and the angle at which it is released.

How is a differential equation for the motion of a pendulum derived?

A differential equation for the motion of a pendulum is derived using Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration. By applying this law to the forces acting on a pendulum, we can derive a differential equation that describes its motion.

What is the significance of a differential equation for the motion of a pendulum?

A differential equation for the motion of a pendulum is significant because it allows us to accurately predict and analyze the behavior of a pendulum. It can be used to determine the maximum height and speed of the pendulum, as well as the period and frequency of its oscillations.

How does the length of a pendulum affect its differential equation for motion?

The length of a pendulum directly affects its differential equation for motion. As the length increases, the period of oscillation also increases, resulting in a longer time for the pendulum to complete one full swing. This change in period is reflected in the coefficients of the differential equation.

Can a differential equation for the motion of a pendulum be solved analytically?

Yes, a differential equation for the motion of a pendulum can be solved analytically using techniques such as separation of variables, integrating factors, and trigonometric identities. These solutions can then be used to accurately predict the behavior of a pendulum under different conditions.

Similar threads

I Solutions to Simple Harmonic Motion second order differential equation
Replies
1
Views
810
A Modeling the damping of a physical rigid pendulum
Replies
1
Views
905
I Solving for the Motion of a Spring Pendulum
3
Replies
76
Views
5K
Two different equations of motion from the same Lagrangian?
Replies
1
Views
1K
Vertical beam on a frictionless surface
Replies
9
Views
2K
Component forces of a pendulum
Replies
2
Views
1K
Simple Harmonic Motion: why sin(wt) instead of sin(t)?
Replies
3
Views
6K
I Why are there 2s -1 independent integrals of motion?
Replies
4
Views
1K
How to parametrize motion of a pendulum in terms of Cartesian coordinates?
Replies
1
Views
543
What is the Missing Component in the Equation of Motion for the Asimov Pendulum?
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top