VM-EXD-MECH-007
VM-EXD-MECH-007
Simple Pendulum with Simple Harmonic Motion (SHM)
Overview
| Reference: | Any Basic Kinematics Book |
| Analysis Type(s): |
Explicit Dynamics 3-D (Fully Rigid) |
| Elements: | Rigid Body Elements |
| Boundary Conditions: | Fixed Constraint, Joint Load |
| Structural Interactions: | No |
| Fluid-Structure Interactions: | No |
| Connections: | Revolute Joint |
| Materials: | Steel |
Test Case
A simple pendulum has a simple harmonic motion (SHM) about its hinged point:
The SHM is given by θ = 1.571*sin (0.5235*t) rad. The hinge point coordinates are (0, 0, -35.56) mm.
The analysis finds the relative angular acceleration of pendulum after t = 3s.
| Material Properties | Geometric Properties | Loading |
|---|---|---|
|
E = 2000000 MPa ν = 0.3 | Hinge point = (0, 0, -35.56) mm | Rotation θ = 1.571*sin (0.5235*t) rad |
Analysis
The pendulum undergoes SHM in the X-Z plane about the hinge.
The angular acceleration of pendulum is given by:
Results Comparison
| Results | Target | Explicit Dynamics [1] | Error (%) |
|---|---|---|---|
| Relative angular acceleration of pendulum after t = 3.0031 s (rad/s2) | -0.433 | -0.43392 | 0.212 |
To compare this result to that obtained using rigid body dynamics, see VM-WB-MECH-053.