KE PE
| For small angles, θ ≅ sin θ, a pendulum undergoes SHM (Simple Harmonic Motion). SHM is a special type of |
| motion that results when a body undergoes repeated motion back and forth about an equilibrium position. |
| In the pendulum animation above, the force in blue is called the restoring force. This restoring force must be directly |
| proportional to the displacement from the equilibrium position. As a result of the restoring force, there is an |
| acceleration also toward the equilibrium position. The red downward force is the weight suspended from the bottom of |
| the string and the longer red force is the force the string exerts on the mass. |
| The two bar graphs, KE and PE, demonstrate the conversion between the kinetic energy and the gravitational |
| potential energy. |
| Because a pendulum's motion repeats itself at regular intervals, the motion is also periodic. The time needed for one |
| complete vibration is called the period, T. A complete vibration is measured from a given displacement and velocity |
back to the same displacement and velocity. A pendulum starting at its right most amplitude swinging through the |
| equilibrium position, to its left most amplitude, is considered one complete vibration or oscillation. The number of |
| complete vibrations or oscillations is measured in units, osc/s = vib/s = Hz, where Hz is hertz. |
| 1) (a) What must be the length of a pendulum to produce a period of 1.0 s? |
| (b) How would you modify a pendulum to produce a period of 1.0 s on the surface of the moon, where |
| gm = 1/6 x ge? |
| 2) (a) Determine the period and frequency of the pendulum in the animation. |
| (b) When is the pendulum moving the fastest and what is its acceleration at that point? |
| 3) Why doesn't the mass of the pendulum bob affect the period of a pendulum? |
| 4) Why doesn't the amplitude affect the period of a pendulum for small angles? |
| 5) Using the conservation of energy, show that vmax = (2gh)1/2. |