Hooke’s LawFs = -kx

K is the spring constant, relates to the stiffness of the spring

The negative in front of the k shows that the force is always in the opposite direction as x.

A Slinky has a spring constant of about 1 N/m, a spring in a car’s suspension can have a spring constant of about 1 E 5 N/m

Spring ProblemsA 76 N crate is hung from a spring (k = 450

N/m) How much does the spring stretch?

A spring of k = 1962 N/m loses its elasticity if stretched more than .50 m. What is the largest mass that can be hung from this spring without damaging the spring?

Spring ProblemsA 76 N crate is hung from a spring (k = 450

N/m) How much does the spring stretch? About 17 cm

A spring of k = 1962 N/m loses its elasticity if stretched more than .50 m. What is the largest mass that can be hung from this spring without damaging the spring? Using hooke’s law, max force is 981 N. Therefore, anything more than about 100 kg would damage the spring.

OscillationsSprings oscillate in

simple harmonic motion

Undamped springs will continue to oscillate

 simple harmonic motion is a type of periodic motion where the restoring force is directly proportional to the displacement.

OscillationsDamped springs will

eventually come to rest

Damping is an influence within or upon an oscillatory system that has the effect of reducing, restricting or preventing its oscillations. 

Equations for Spring Problems:

In absence of external forces such as friction: E= Us + K

At max x or equilibrium positions: ½ mv2 = ½ kx2

Period of motion:

Equations for Pendulum Problems:

In absence of external forces such as friction: E= Ug + K

At max h or min h positions: ½ mv2 = mgh

Period of motion:

Oscillations1. Equilibrium

x = 0 F = 0, a = o v = + max

2. Max positive displacement x = + max F = - max, a = - max v = 0

3. Equilibrium x = 0 F = 0, a = 0 v = - max

4. Max negative displacement x = - max F = + max, a = + max v = 0

5. Equilibrium x = 0 F = 0, a = 0 v = + max

Period vs. FrequencyPeriod is how long it takes to complete one

cycle (seconds per cycle)Frequency is how many cycles it completes in

a unit of time, usually 1 second (cycles per second)

f = 1/T or T = 1/fSI unit for period – secondsSI unit for frequency – Hertz, HzHz= 1/s

Period vs. FrequencyA spring makes a complete cycle every 3

seconds, what is its frequency?A spring has a frequency of 20 Hz, what is its

period?

The period of a Spring-Mass System

If you hang a 2kg mass from a spring constant of 25 N/m, what is the period?

A Test-Like QuestionAt equilibrium 6 N weight stretches a spring

0.5 m. If the spring mass system begins to oscillate, what will be its period?

F = kx

PendulumsDepends on the length of the pendulum and

surface gravity.

Pendulums were used as the first way to accurately determine surface gravity

EquationsSpring-Mass Pendulum

ProblemHow long is the period of a pendulum that is

0.75m long?

If that pendulum is moved to the moon (g = 1.62), what will its new period be?