Chapter 11 Quick notes 11-1 through 11-4
1. Periodic motion (simple harmonic motion) is the vibration or oscillation of
an object over the same path in the same amount of time.
2. Hooke’s Law
F=-kx
The restoring force is equal to the displacement x of the spring from
the equilibrium position
3. As an object oscillates the velocity is zero at the furthest displacements from
equilibrium (+A and –A) and are the max at the equilibrium position.
4. As an object oscillates the Acceleration and force are max at the furthest
displacements from equilibrium (+A and –A) and are zero at the equilibrium
position.
5. Amplitude is the maximum displacement from the equilibrium point
6. One cycle is the to and from motion back to the original point.
7. Period (T)is the time it takes to complete one cycle
8. Frequency (f) is the number of cycles in one second
a. f=1/T and T=1/f
9. A spring in the vertical position with a mass will have a new equilibrium
position due to gravity
10. Simple harmonic oscillators are system that the net restoring force is
proportional to the negative of the displacement
11-2
1. Energy in SHM continuously changes from kinetic to potential and back again
2. At the amplitudes, ME= ½ kA2
3. at x=0 (the equilibrium point)
ME= ½ mv2max
4. At intermediate points
½ mv2 + ½ kx2 = ½ kA2
5. Velocity of an object at x distance would then be: v = +/- vmax (1-x2/A2}
11-3
1. Period of an SHO is dependent on the mass and the stiffness of the spring but
not on the amplitude! T=2[m/k] i.e. larger the mass the > the period. the
stiffer the spring the shorter the period.
2. f =1/2[k/m]
3. When considering position as a function of time: x= A cos (2t/T)=A cos 2f
=Acost
4. Curves can be both sin and cosine dependent on starting as x = 0 vs x=A and
the curve is sinusoidal.
5. velocity=-vmaxsint = =-vmaxsin (2ft) = =-vmaxsin (2t/T)
6. Acceleration = -kx/m = -(kA/m)cost = -amaxcos (2t/T)
Simple Pendulum
1. Period of a simple pendulum: T = 2l/g
2. Frequency: f = 1/2g/l
3. Mass of the bob is not important
On your white boards let’s go through the sample problems in the book.
On your own or with a partner, do problems 3, 7,13, 23, 27 and 29