1. Simple Harmonic Motion (SHM)
Chapter 11: Section 1
Simple Harmonic Motion (SHM)

2. Periodic Motion
A repeated motion that moves back and forth over the same path.
Examples include: pendulum, vibrating string, orbiting planet

3. Simple Harmonic Motion (SHM)
A special kind of periodic motion
Results from a restoring force that is proportional to displacement.
Restoring Force: force that tries to reestablish equilibrium.
During SHM, an object oscillates (vibrates back and forth) around a central equilibrium position.

4. Springs: stretching m m -Fs
When you stretch a spring, you must apply an increasing amount of force as the displacement increases.
That means the spring is pulling back with an equal and opposite force m m x
-Fs

5. Springs: compressing m m
When you compress a spring, you must apply an increasing amount of force as the displacement increases.
That means the spring is pushing back with an equal and opposite force m m x Fs

6. Displaced Position
-Force is at maximum
-Since F=ma a = max
-v = 0
Equilibrium Position
-Net Force= 0
-Since F=ma a =0
-v = maximum

7. Felastic= - k Δ x Hook’s Law
K = Spring Constant (measures stiffness of spring)
Δ x = displacement from equilibirum)
- sign indicates that the force is opposite displacement

8. A stretched or compressed spring has elastic potential energy.
Work needed to stretch or compress a string:
W=½ kΔx2
Since work = change in PE
PE =½ kΔx2
Taking various forms of energy into account, the total energy is given by:
E = ½ mv2 + mgh + ½ kΔx2

9. Sample Problem
If a mass of 0.25 kg attached to a vertical spring stretches the spring 3.0 cm from its equilibrium position, what is the spring constant?

11. Sample problem
A 1.80 kg object is connected to a spring of force constant 120 N/m. How far is the spring stretched if it is used to drag the object across a floor at constant velocity? Assume the coefficient of kinetic friction is 0.60.

13. A Simple Pendulum Consists of a mass, called a bob
The restoring force of a pendulum is a component of the bob’s weight.
When the angle is <15 degrees, the restoring force is proportional to the displacement.
For small angles, the pendulum’s motion is simple harmonic.

14. A Simple Pendulum Cont.
Please note: FT = tension force, F r = restoring force and U is another symbol for Potential Energy