Simple harmonic motion HELP ME!! (1 Viewer)

[star*eyed]

could someone please help me with the following question. can u please explain each step cause i have NO idea!


x= 3cos (2pi t)
determine the greatest displacement, velocity and acceleration.

Even help on just one section would be GREATLY appreciated

 

[*Ninny-mole*]

Okay, i'm a dumbass at this subject so I'm not the best person to answer your question. All I know about SHM, is that: x= a sin (n t + E)
v= - a n cos (n t + E)
a= -a n^2 sin (n t + E)
where n and E are constants (i think). Don't take my word for it. But you probably know that too. Sorry, but I have got no clue how to do "find the greatest questions". Sorry. Somebody help her...

 

[SoulSearcher]

x = 3cos(2pi*t)
Greatest value of cos (2pi*t) is 1
Therefore greatest displacement is 3 units from the origin.

v² = n²(a²-x²)
Velocity is greatest when x = 0, n = 2pi, a = 3
v² = 9(4pi²-0)
v² = 36pi²
v = + 6pi
Therefore greatest velocity is 6pi units/second.

a = -n²x
Acceleration is greatest when x = a, when a = 3 in this particular equation
a = -4pi²*3
a = -12pi²
Therefore greatest acceleration is 12pi² units/seconds²

 

[Riviet]

The "greatest" mentioned in the question reminds me of the binomial theorem when you're asked to find the greateset term or coefficient. I'm used to the more conventional way of describing it (usually "maximum").

 

[star*eyed]

Y is the velocity greatest when x=0 ??????????? and the answers in book say acceleration greatest at 12pi^2

and is velocity and acceleratio greatest when a= 3 because that is the greatest displacement???

ahhh i am sooo hopeless at this topic

 

[Riviet]

n=2pi not 3pi.

.'. a=2².3
=4x3
=12

edit: 2pi, not 3pi

 

[SoulSearcher]

Well technically it's 2pi, but meh

 

[star*eyed]

Y is the velocity greatest when x=0 ???????????
and is velocity and acceleratio greatest when a= 3 because that is the greatest displacement???

 

[pLuvia]

Have you tried drawing out graphs for the SHM? Because it would be clearer if you did, but also velocity is also greatest when a=0. Because if acceleration is 0, then the velocity can't speed up, hence it is at its limiting value, hence maximum

 

[cracker barrel]

I was wondering when someone was going to mention that. Graphs are the best way to go for SHM

 

[SoulSearcher]

I was wondering when someone was going to mention that. Graphs are the best way to go for SHM

Graph drawing is good for SHM

 

[vafa]

ok, let me tell you the easiest way. you do not need to know any formulae and you do not need to waste lots of your time to sketch the fucntion.

I know from the question that:

x= 3cos (2pi t)
v=-6pisin(2pit)
a=-12pi^cos(2pit)

hence graetest x=3
greatest velocity/speed= 6pi
greatest a=12pi^2

it took you 3 seconds to get this and you would save your time to do harder question in the exam.