Thursday

October 2, 2014

October 2, 2014

Posted by **shan** on Wednesday, December 12, 2007 at 2:14am.

here is what i have done so far where am i going wrong

V=pie10cos(piet + pie/3)

V^2 = pie^2 100cos^2(piet+ pie/3)

KE = mpie5ocos^2 (piet + pie/3)

X^2 =100sin^2(piet +pie/2 )

PE =k50 sin^2(piet +pie/2 )

KE=PE

pie^2 100cos^2(piet+ pie/3) =K50 sin^2(piet +pie/2 )

m/k * pie^2 = tan^2(piet +pie/2 )

take square root of both sides of equation

1/pie * pie = tan(piet + pie/3)

piet + pie/3 =tan-1(1)

solving for t i get a negative value where iam i going wrong

- physics -
**Damon**, Wednesday, December 12, 2007 at 9:48amYou said pi/2 at first, then changed to pi/3

I assume that we are talking about a spring here so

PE = (1/2)kx^2

then

v = 10 pi cos (pi t + pi/2)

v^2 = 100 pi^2 cos^2 (pi t + pi/2)

KE = (1/2) m v^2 = 50 m pi^2 cos^2(pi t +pi/2)

so sort of agree with you

Now PE = (1/2) k x^2 =

(1/2)k 100 sin^2( pi t + pi/2)

so when does PE = KE?

50 m pi^2 cos^2 pi t + pi/2) =50 k sin^2(pi t + pi/2)

m pi^2 cos^2 = k sin^2

tan^2 (pi t + pi/2 ) =pi^2 m/k

tan (pi t +pi/2) = +/- pi sqrt(m/k)

two solutions:

t =-1/2 + (1/pi)tan^-1(pi sqrt(m/k))

t =-1/2 - (1/pi)tan^-1(pi sqrt(m/k))

Now sqrt (m/k) means something

wo the natural frequency = sqrt (k/m)

= 2 pi fo = 2 pi/T where T is the period of free vibration

so

sqrt (m/k) = T/ 2 pi

so use that

**Answer this Question**

**Related Questions**

Physics - The motion of a particle connected to a spring is described by x=10cos...

Physics - The motion of a particle connected to a spring is described by x= ...

ap calc - a particle moves along the x-axis so that its velocity at any time t ...

ap calc - a particle moves along the x-axis so that its velocity at any time t ...

physics - A body oscillates with simple harmonic motion along the x-axis. Its ...

physics - One particle has a mass of 3.00*10-3 kg and a charge of +7.60 µC...

Physics - A particle with mass 6.4 is acted on by a conservative force moves ...

Physics - A particle with mass 6.4 is acted on by a conservative force moves ...

Physics - The motion of a block-spring system is described by x(t) = A sin(ùt). ...

Physics - A 245 g particle is released from rest at point A inside a smooth ...