1. Oscillations 1. Different types of motion:
Uniform motion
1D motion with constant acceleration
Projectile motion
Circular motion
Oscillations
2. Different types of oscillations:
Periodic oscillations
A motion is called periodic when the system comes back to the same physical conditions every time interval T.
Harmonic oscillations (the simplest, the most important type of periodic oscillations)
Chaotic oscillations

2. 3. Harmonic oscillations
Relation between circular motion and simple harmonic oscillations y
R=A x
linear equation
Period of SHO is independent from amplitude!

3. T x
A=xmax t v t a t

4. 4. Hook’s law and simple harmonic motion
Newton’s second law:
Simple harmonic motion:
Question: Two identical masses hang from two identical springs. In case 1, the mass is pulled down 2 cm and released.
In case 2, the mass is pulled down 4 cm and released.
How do the periods of their motions compare?
A. T1 < T2 B. T1 = T2 C. T1 > T2
Period is independent of amplitude!
This is in fact general to all SHM (not only for springs)!

5. x t 5. The simple pendulum mg L If than Units: Example:
Independent from
amplitude!
Units:
Example:

6. Example: A person swings on a swing
Example: A person swings on a swing. When the person sits still, the swing
moves back and forth at its natural frequency. If, instead, the person stands
on the swing, the new natural frequency of the swing is:
A. Greater B. The same C. Smaller
If the person stands, L becomes smaller
Example: Grandpa decides to move to the Moon, and he naturally takes his old pendulum clock with him. But gravity on the Moon is approximately g/6... As a result, his clock is:
A. Too fast B. Too slow
C. Too fast until Noon, too slow after noon
The period of the pendulum is longer on the Moon. So each “second according to this clock” is then longer than a real second.
To tune the clock you can move the clock’s disk up.

7. Question: Mass m attached to a spring with a spring constant k
Question: Mass m attached to a spring with a spring constant k. If the mass m increases by a factor of 4, the frequency of oscillation of the mass
is doubled
is multiplied by a factor of 4
is halved
is multiplied by a factor of 1/4
Question: A 2.0 kg mass attached to a spring with a spring constant of 200 N/m. The angular frequency of oscillation of the mass is __ rad/s.
A. 2 B C. 60 D. 100

8. 6. Energy in the simple harmonic motionU x E –A A K t U t E t
Total mechanical energy is constant through
oscillation: conservation of energy!

9. 7. Damped Harmonic Motion
x(t) t

10. 8. Resonance