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Key equations

Relationship between frequency and period f = 1 T
Position in SHM with ϕ = 0.00 x ( t ) = A cos ( ω t )
General position in SHM x ( t ) = A cos ( ω t + ϕ )
General velocity in SHM v ( t ) = A ω sin ( ω t + ϕ )
General acceleration in SHM a ( t ) = A ω 2 cos ( ω t + ϕ )
Maximum displacement (amplitude) of SHM x max = A
Maximum velocity of SHM | v max | = A ω
Maximum acceleration of SHM | a max | = A ω 2
Angular frequency of a mass-spring system in SHM ω = k m
Period of a mass-spring system in SHM T = 2 π m k
Frequency of a mass-spring system in SHM f = 1 2 π k m
Energy in a mass-spring system in SHM E Total = 1 2 k x 2 + 1 2 m v 2 = 1 2 k A 2
The velocity of the mass in a spring-mass
system in SHM
v = ± k m ( A 2 x 2 )
The x -component of the radius of a rotating disk x ( t ) = A cos ( ω t + ϕ )
The x -component of the velocity of the edge of a rotating disk v ( t ) = v max sin ( ω t + ϕ )
The x -component of the acceleration of the
edge of a rotating disk
a ( t ) = a max cos ( ω t + ϕ )
Force equation for a simple pendulum d 2 θ d t 2 = g L θ
Angular frequency for a simple pendulum ω = g L
Period of a simple pendulum T = 2 π L g
Angular frequency of a physical pendulum ω = m g L I
Period of a physical pendulum T = 2 π I m g L
Period of a torsional pendulum T = 2 π I κ
Newton’s second law for harmonic motion m d 2 x d t 2 + b d x d t + k x = 0
Solution for underdamped harmonic motion x ( t ) = A 0 e b 2 m t cos ( ω t + ϕ )
Natural angular frequency of a
mass-spring system
ω 0 = k m
Angular frequency of underdamped
harmonic motion
ω = ω 0 2 ( b 2 m ) 2
Newton’s second law for forced,
damped oscillation
k x b d x d t + F o sin ( ω t ) = m d 2 x d t 2
Solution to Newton’s second law for forced,
damped oscillations
x ( t ) = A cos ( ω t + ϕ )
Amplitude of system undergoing forced,
damped oscillations
A = F o m ( ω 2 ω o 2 ) 2 + b 2 ω 2

Conceptual questions

Why are soldiers in general ordered to “route step” (walk out of step) across a bridge?

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Do you think there is any harmonic motion in the physical world that is not damped harmonic motion? Try to make a list of five examples of undamped harmonic motion and damped harmonic motion. Which list was easier to make?

All harmonic motion is damped harmonic motion, but the damping may be negligible. This is due to friction and drag forces. It is easy to come up with five examples of damped motion: (1) A mass oscillating on a hanging on a spring (it eventually comes to rest). (2) Shock absorbers in a car (thankfully they also come to rest). (3) A pendulum is a grandfather clock (weights are added to add energy to the oscillations). (4) A child on a swing (eventually comes to rest unless energy is added by pushing the child). (5) A marble rolling in a bowl (eventually comes to rest). As for the undamped motion, even a mass on a spring in a vacuum will eventually come to rest due to internal forces in the spring. Damping may be negligible, but cannot be eliminated.

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Some engineers use sound to diagnose performance problems with car engines. Occasionally, a part of the engine is designed that resonates at the frequency of the engine. The unwanted oscillations can cause noise that irritates the driver or could lead to the part failing prematurely. In one case, a part was located that had a length L made of a material with a mass M . What can be done to correct this problem?

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Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
what is titration
John Reply
what is physics
Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
what is the dimension formula of energy?
David Reply
what is viscosity?
David
what is inorganic
emma Reply
what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
what's motion
Maurice Reply
what are the types of wave
Maurice
answer
Magreth
progressive wave
Magreth
hello friend how are you
Muhammad Reply
fine, how about you?
Mohammed
hi
Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
Who can show me the full solution in this problem?
Reofrir Reply
Practice Key Terms 1

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Source:  OpenStax, University physics volume 1. OpenStax CNX. Sep 19, 2016 Download for free at http://cnx.org/content/col12031/1.5
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