Oscillations

1
Oscillations

• Kinematics - sinusoidal waves
• Dynamics -Newtons law and Hookes law.
• Energetics Conservation of Energy
• Mass on a spring
• Pendulum

2
Oscillations

• repetitive displacements with a time period
• provide the basis for measuring time
• serve as the starting point for describing
• wave motion.
• Example- Mass on a spring

3
Mass on a Spring

• Hookes Law -Force
• exerted by spring is
• proportional to the
• displacement from the
• equilibrium position.
• F -kx
• k - Force constant
• Units N/m

4
Hookes Law
5
Vertical direction

• The force of gravity is
• cancelled by the force
• of the spring.
• Equilibrium position ?
• The force on the object when it is displaced
  upward
• by a distance y from the equilibrium position is
  only
• Due to the spring. Fy -ky mg

6
Dynamics
7
The restoring force is proportional to the
displacement for small displacements. F
-mgsin? F -mg? for small ? F - mgs
L Equivalent to Hookes Law
with kmg/L ? v(k/m ) then becomes ?
v(g/L ) Tpendulum 2p v(L/g)
The period is dependent on
L T 1/f but independent
of m
8

• For SHM, you can apply the second law to get
• F - Kx ma
• a - (K/m)x

X R cos? a (v2/R)cos ? A (v2/R2)(Rcos ?)
v2/R2)x
9

• For a reference circle
• 2pA v0T T (2pA)/v0
• Ei Ef ½ kA2 ½ mv02 A/v0
  v(m/k)
• Tspring 2p v(m/k)