Need some help! (1 Viewer)

[lacklustre]

Like usual I have a few questions I can't do.

1. Given that x = asin(nt+α), find v as a function of time (<--this part i can do). Find a, n and α if a>0, n>0, 0≤α<2pi and:

a) the period is 6 seconds, and initially x=0 and v=5.


2. Particle moving in S.H.M. has period pi/2 seconds. Initially the particle is at x=3 with velocity v=16m/s.

a) Find x as function of t in form x = bsin nt + c cosnt (<-- i was able to do this)
b) Find x as a function of t in the form x = acos(nt-ε), where a>0 and 0≤ε<2pi.

Cheers.

 

[vds700]

Like usual I have a few questions I can't do.

1. Given that x = asin(nt+ x=), find v as a function of time (<--this part i can do). Find a, n and α if a>0, n>0, 0≤α<2pi and:

a) the period is 6 seconds, and initially x=0 and v=5.


2. Particle moving in S.H.M. has period pi/2 seconds. Initially the particle is at x=3 with velocity v=16m/s.

a) Find x as function of t in form x = bsin nt + c cosnt (<-- i was able to do this)
b) Find x as a function of t in the form x = acos(nt-ε), where a>0 and 0≤ε<2pi.

Cheers.

1. x = asin(nt + α) when t = 0, x = 0
asinα = 0
sinα = 0
therefore α = 0.
Period: T = 2pi/n = 6
n = 2pi/6 = pi/3
v = (pi/3)acos (pi/3)t
when t = 0, v = 5
(pi/3)acos0 = 5
(pi/3)a = 5
a = 15/pi

 

[lacklustre]

1. x = asin(nt + α) when t = 0, x = 0
asinα = 0
sinα = 0
therefore α = 0.
Period: T = 2pi/n = 6
n = 2pi/6 = pi/3
v = (pi/3)acos (pi/3)t
when t = 0, v = 5
(pi/3)acos0 = 5
(pi/3)a = 5
a = 15/pi

Cool, I get it. Thanks vds.

Can anybody do the second part?

 

[vds700]

Cool, I get it. Thanks vds.

Can anybody do the second part?

ok for 2b, u can either use trigonometric transformations to get your answer from into the required form or...

let x = asin(nt + α), v = nacos(nt + α)

T = 2pi/n = pi/2
n = 4
when t =0, x = 3,
3 = asinα ....eq 1
when t = 0, x = 16
16 = 4acosα
4 = acosα ... eq 2.

eq1/eq2
tanα = 3/4
α = arctan(3/4)

square and add 1 and 2
a^2sin^2α + a^2cos^2α = 25
a^2 = 25
a = 5

therefore x = 5sin(4t + arctan(3/4))

 

[lacklustre]

Another problem. Same question different part:

1. Given that x = asin(nt+α), find v as a function of time (<--this part i can do). Find a, n and α if a>0, n>0, 0≤α<2pi and:

c) the period is 2pi seconds and initially x=1 and v=-1.

Here's what i've done:

T=2pi=2pi/n
n=1
when t=0 : x=1, v=-1 so:
asinα=1
sinα=1/a

-1=acosα
cosα=-1/a

Where do I go from here to find the amplitude and initial phase? The other ones were easy for me because usually i'd get an equation that equalled 0 and it eliminated some variables so i could find alpha.

 

[vds700]

Another problem. Same question different part:

1. Given that x = asin(nt+α), find v as a function of time (<--this part i can do). Find a, n and α if a>0, n>0, 0≤α<2pi and:

c) the period is 2pi seconds and initially x=1 and v=-1.

Here's what i've done:

T=2pi=2pi/n
n=1
when t=0 : x=1, v=-1 so:
asinα=1
sinα=1/a

-1=acosα
cosα=-1/a

Where do I go from here to find the amplitude and initial phase? The other ones were easy for me because usually i'd get an equation that equalled 0 and it eliminated some variables so i could find alpha.

asinα/acosα = -1
tanα = -1
α =-pi/4
a^sin^2α + a^2cos^2α = 2
a^2 = 2
a =root2

 

[lacklustre]

asinα/acosα = -1
tanα = -1
α =-pi/4
a^sin^2α + a^2cos^2α = 2
a^2 = 2
a =root2

Jeez thanks man. You are my saviour.

 

[lacklustre]

hey will. your not around here often

Oh I'm here alright. I just lurk around.