1. Simple Harmonic Motion

2. Oscillations
Oscillation or vibration – the motion of an object that regularly repeats itself, back and forth, over the same path.
That motion is periodic, meaning it has
a certain frequency and period.
Mass on a spring
Particle moving in uniform circular motion
Me walking down lecture hall steps

3. Springs and Simple Harmonic Motion
Recall the spring:

4. Circles and Simple Harmonic Motion
A fundamental parallel can be drawn between SHM (mass on a spring), and uniform circular motion.
What is ω for a spring?

5. Circles and Simple Harmonic Motion
A fundamental parallel can be drawn between SHM (mass on a spring), and uniform circular motion.

6. Position Conceptualized
Depending upon the initial conditions…

7. Velocity

8. Acceleration

9. All together now…

10. Example
As mass-spring system oscillates with an amplitude of 3.0 cm. If the spring constant is 270 N/m and object has a mass of 0.50 kg, determine the period, the maximum speed and maximum acceleration of the mass.
3.0 cm

11. The Pendulum

12. The Pendulum

13. Example
A simple pendulum has a length of 52.3 cm and makes 83.9 complete oscillations in 2.00 min after being pulled to the side by 0.25m.
Find the period of the pendulum, the acceleration due to gravity at the location of the pendulum, and the maximum speed of the pendulum.

14. Grandfather Clock
Your grandfather clock is running slowly. Every 24 hours, you find that it has lost 2 minutes. How will you fix this problem?
Shorten the pendulum by 3 mm.