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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=
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