Solved: Harmonic Motion - A, T, v=0, Acceleration, & Phase

[BlueRiboon]

Homework Statement

The motion of a particle is given by: x = (6.0m) cos(0.586t + 0.72)

a) Find the amplitude
b) Find the Period
c) Find the first time for t>0 when v=0
d) Find the maximum acceleration
e) Fine the phase at time t=1.38s

Homework Equations

x = A cos ωt
T = 2pi/ω
f = 1/T

The Attempt at a Solution

I am taking the course on Online, there is no online lecture..
Have to learn everything from the textbook but, English is my second language :'(
Having hard time understand the basic concept..

a) A = 6.0

b) I don't know about 0.586t + 0.72
should I just calculate like.. T = 2pi / ω , T =2pi/0.586 ?
Where do I use 0.72?

c) v=0 (t>0) it means, fine the time at T/2 ?

d) no idea..

e) is phase means to find x ? so just plug t=1.38 in the formula?


Thank you so much for your help.. quicker the better..

I am not even done with studying everything , but have a final exam in 2 days.
.. I started the course 5 weeks ago with another offline course.. (due to school's cancellation of my course) , and so far finished 12 chapters.., 2 more chapters to go!

Any help would be so appreciated!
Thanks!

 

[lewando]

Try exploring this equation by plotting it [fooplot.com provides a nice tool].
For d), you are given x(t). v(t) = dx(t)/dt, a(t) = dv(t)/dt.

 

[BlueRiboon]

Try exploring this equation by plotting it [fooplot.com provides a nice tool].
For d), you are given x(t). v(t) = dx(t)/dt, a(t) = dv(t)/dt.

Thank you for your reply

I tried plotting it that website,

For a) b) d) , After I plotting on the website, I think +0.72 just shift whole thing to the right,
so won't effect the amplitude, period and max Accelation.

If my assumption is correct, I got the a,b,d but still have no idea about c)
and, for e) do I just have to put time in the equation?

Thanks!

 

[PeterO]

Homework Statement

The motion of a particle is given by: x = (6.0m) cos(0.586t + 0.72)

a) Find the amplitude
b) Find the Period
c) Find the first time for t>0 when v=0
d) Find the maximum acceleration
e) Fine the phase at time t=1.38s

Homework Equations

x = A cos ωt
T = 2pi/ω
f = 1/T

The Attempt at a Solution

I am taking the course on Online, there is no online lecture..
Have to learn everything from the textbook but, English is my second language :'(
Having hard time understand the basic concept..

a) A = 6.0

b) I don't know about 0.586t + 0.72
should I just calculate like.. T = 2pi / ω , T =2pi/0.586 ?
Where do I use 0.72?

c) v=0 (t>0) it means, fine the time at T/2 ?

d) no idea..

e) is phase means to find x ? so just plug t=1.38 in the formula?


Thank you so much for your help.. quicker the better..

I am not even done with studying everything , but have a final exam in 2 days.
.. I started the course 5 weeks ago with another offline course.. (due to school's cancellation of my course) , and so far finished 12 chapters.., 2 more chapters to go!

Any help would be so appreciated!
Thanks!

b) If a weighted spring was set in oscillation in shm, and you then walked into the room and watched it - what is to say it was passing through the equilibrium position at the instant you walked in? The 0.72 is the factor necessary for the mathematical description to match what you actually observed - so you proposal for calculating T looks good.

c) v=0 occurs at maximum displacement - so when cos(...) = 1 and -1. What is the smallest positive value of t that meets those conditions.

d) maximum acceleration occurs at maximum displacement, though using calculus [derivatives] as suggested by lewando is probably called for.

e) not quite sure what is meant by this.