1. Simple Harmonic Motion

2. PhET mass spring applet

3. A 4. 0-kg object is attached to a spring of spring constant 10 N/m
A 4.0-kg object is attached to a spring of spring constant 10 N/m. The object is displaced by 5.0 cm from the equilibrium position and let go. What is the period of vibration?

4. Oscillations Are about continuous mechanical energy transformations…
Between Kinetic Energy
and Potential Energy
The total mechanical energy is:
Where A = xmax

5. Ek and Ep

6. Spring Period (Energy proof) v
vmax -A +A

7. A 0.50-kg mass is attached to a spring of spring constant 20 N/m along a horizontal, frictionless surface. The object oscillates in simple harmonic motion and has a speed of 1.5 m/s at the equilibrium position. What is the total energy of the system?

8. A 0.50-kg mass is attached to a spring of spring constant 20 N/m along a horizontal, frictionless surface. The object oscillates in simple harmonic motion and has a speed of 1.5 m/s at the equilibrium position. What is the amplitude of vibration?

9. A 0. 30-kg mass is suspended on a spring
A 0.30-kg mass is suspended on a spring. In equilibrium the mass stretches the spring 2.0 cm downward. The mass is then pulled an additional distance of 1.0 cm down and released from rest. Calculate the total energy of the system.

10. Spring Period (Forces / Motion proof)-A +A

11. Web Link: Simple Harmonic Motion
time
If the masses are all the same, which spring has the greatest spring constant?
Black
Green
Blue
Web Link: Simple Harmonic Motion

12. It has Simple Harmonic Motion!
The Pendulum
It has Simple Harmonic Motion!
Where is the speed maximum?
Where is the speed minimum?
Use a free body diagram to find the torque on the mass

13. The frequency of a pendulum
9.8 m/s2
Length of pendulum (to center of mass)
*   10
* Independent of mass
Web Link: Simple Harmonic Motion

14. A person swings on a swing
A person swings on a swing. When the person is seated, the swing oscillates back and forth at its natural frequency. If, instead, the person stands on the swing, the new natural frequency of the swing is
1. greater
2. the same
3. smaller

15. A simple pendulum and a mass hanging on a spring both have a period of 1 s when set into small oscillatory motion on Earth. They are taken to Planet X, which has the same diameter as Earth but twice the mass. Which of the following statements is true about the periods of the two objects on Planet X compared to their periods on Earth?
(a) Both are shorter.
(b) Both are the same.
(c) Both are longer.
(d) The period of the mass on the spring is shorter, while the pendulum is the same.
(e) The period of the pendulum is shorter, while the mass on the spring is the same.

16. A simple pendulum consists of a mass at the end of a lightweight cord
A simple pendulum consists of a mass at the end of a lightweight cord. We assume that the cord does not stretch, and that its mass is negligible. q L T s x m q F mg