SHM chaoter 17 Flashcards
What is SIMPLE harmonic motion
When motion oscilallte about an equilborum position
Where the acceleration of this motion is always proportional to negative displacement, thus oppsite the direction of motion, such that it always acts towards the equilibrium position
What is angular frequency
A CONSTSNT per system, but is not NORMAL frewuency, lit all we have to know is it’s omega and = 2Pi/ T or 2Pif, although in normal circular motion systems angular velocity and angular frequency twke the same values, in general angualr velocity can be a different value
JUST DONT LACK, if they ask for angular frequency then only take OMEGA
Why else can angular frewuency still be applied even if nothing is physically moving
Can be shown for ac current, so basically a constant for anything that has OSCILLATIONs in its motion
When do you use which displace the formual and how to derrive
Based on starting position, if at 0 then sin if at 1 then cos
Derrive using cos graoh, and replace theta with omega t so it’s a function of time
Now just differntiate and you’ll see accerlwtion prodptimsl to - displamcent , where kind omega sqaured
Max accerlwtion velocitied etc
Max accerlwtion happens at max amplitude
Max velocity happens at equilborum position , as itd 0 velocity at max acceleration
What is the phase difference between the displacement velocity and accerlwtion rbosdh
Pi / 2 and pi from displacement to acclergwion, just draw and you’ll see
IMPORTANT ! Time period is affected by what?
NOTHING , time period is INDEPENDENT OF AMPLITUDE, only dependent on the constants in system such as length, spring CONSTSNT, g , mass etc
Therefore don’t lack, they are always ISOCHRONUS, even when damping it doesntchange
How to use graphs to show when v is max and a is max?
We know grsdient of graphs = to velocity and a. So when grsdient is max, we have max.
Grsdient is max at equilborum so when dsiaplcent is 0 velocity id max, and lowest when displacement is highest etc etc
Energy about when a spring is always in tension
Therefore spring will always have epe, no matter where it is. But a t we will have min ke as usual . Going up gpe increasing but epe decreasing all the time, ke is max at bottom and top
If doing work , then ke decreases too, total energy of system decreased
Damping
Light damping is like air, reduced amplitude as energy decreases ( and energy is linked), however time period same
Critical is brings to equilborum quickest
Heavy makes nonoscislltions but takes time
Yiu have a car, yiu want criticsl damping do that you get to equilborum wucikest snd feel lesst smoiunt if bounced
Damoenign is when an asxternalforce does workntidecrease the wmokriures of the oscislltiosj
Free vs firced oscislltions and resonance
When an oscislltor is allowed to vibrate freely, this is free oscislltiosn. It will have anstrahlest frewuency which is dependent on internal fsctord
A mechanical oscislltor can cause the system to perform shm at a specific frequency. As this frewuency is increased closer tk natural frequency, it increases in amplitude until max at natural
At this point it resonates. Redosnnance is when the freuwney ifdriving oscislltor matched the frewuency of the free oscislltor natural. At thid point MAXIMUM energy transfer occurs between the mechanical and the normal, and so maximum amplitude is increased
Under damping, the max amplitude decreases, AND THE FREWUENCY AT WHICH THE MAX OCCURD SHIFTS TO THE LEFT ,( even tho natural stays the same )
How could Resonanzen occur with brudges
If the driving FORCE frewuency caused by wind or Periode walking matches the natural f of the bridge it could cause it to resoannt, and so vibrate with maximum amoktoufe This could causes rstesses on the sturctusl components and cause ti to collapse potentially .e.
How to talk about driving force
When frewuency of the DRIVING FORCE… and provide examples
Why does dampening reduce the amplitudes
External force applied, work must be done agaisnt this force, therefore energy leaves the system and so max amplitude decreases , energy leaves in the form of heat
