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simple harmonic motion

motion that is repeated because displacement and restoring force are proportional

Hooke's law

Fs= -kx

stiff spring has

greater k value

opposite direction

Fs and X have

during oscillation

force on block= 0

@ endpoint,

restoring force/magnitude the greatest

What causes the oscillation

Elastic potential energy transform into kinetic energy, then transform back to potential energy

Us

1/2 kx^2

farther stretch/compress

more work, more potental energy

x=xmax

x=A

1/2 kx^2

1/2 kA^2= 1/2 mv^2

T (period)

amount of time it takes to complete a cycle

f (frequency)

# of cycles that can be completed. Hz

T

1/f

f

1/T

Simple harmonic motion is independent of

amplitude. because F is proportional to x

vertical motion oscillator

gravity causes the block to move downward

F=

(-mass x initial velocity) / time

Kd=

mg

mg/k

d (distance how far it stretched)=

F(restoring)

mg sin(theta)

endpoints have

greatest magnitude in restoring force/acceleration

KE goes up

pass through equil position,

T=

2 pi radical (L/G)

frequency and period

don't depend on amplitude/mass

Spring Restoring Force

The force that causes a disturbed system to tend back towards its equilibrium position.

0

example of a saturated fat with single carbon bonds

Relaxed length of a spring?

The length of the spring in its equilibrium position. The length it wants to be.

more force must be applied.

To cause a larger displacement of a spring _______

What does the spring constant k tell us about the properties of the spring?

A larger k means it's more stiff and therefore more force is needed to move it.

x = L - L₀

What is x in the Hooke's Law?

Oscillation means to move back and forth.

Oscillation means? What is another name for it? This time of motion is?

Equilibrium Position?

The resting position an oscillating object wants to assume.

Damping

An influence that causes an oscillating object to lose energy and eventually come to a rest on its own.

In the case of a pendulum or spring the amplitude is?

The maximum distance the object is displaced from its resting position.

period

Time for one revolution

w=2π/T or

Find angular frequency

Frequency

#cycles/second

ƒ=1/2π√(k/m)

Frequency from spring-block oscillator

T=2π√(m/k)

Period from spring-block oscillator

x(t)=Asin(wt + ∅₀)

Position of sinusoidal simple harmonic motion

∅₀=sin⁻¹(x(t=0)/A)

Find ∅₀

v(t)=Awcos(wt+∅₀)

Velocity of sinusoidal simple harmonic motion

a(t)=-Aw²(wt+∅₀)

Acceleration of sinusoidal SHM

a(t)=-w²*x(t)

Important acceleration

v = wA

Maximum velocity and acceleration

Potential Energy

(mass) x (g) x (height)

kinetic energy

a running dog

E=U+K=1/2kA²

Total Mechanical Energy

ag = 8π²L/3T²

Acceleration of gravity for pendulum

T=2π√L/g

Period for simple pendulum