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April 16, 2014

April 16, 2014

Posted by **sunny** on Monday, December 31, 2012 at 6:29pm.

What spring constant should be used if it is to oscillate correctly?

k = N/m

An equation of the form x(t)=Xmax cos(ωt) can be used to describe the motion of this spring-mass system. From the data given, determine the values of Xmax and ω.

Xmax = m

ω = rad/sec

An equation of the form v(t)= Vmax sin(ω2t) can be used to describe the velocity of this spring-mass system. From the data given, determine the values of Vmax and ω2.

Vmax = m/s

ω2 = rad/sec

An equation of the form a(t)=amax cos(ω3t) can be used to describe the acceleration of this spring-mass system. From the data given, determine the values of amax and ω3.

amax = m/s2

ω3 = rad/sec

- physics -
**Damon**, Monday, December 31, 2012 at 7:09pmperiod T = 12 seconds

amplitude = 1.2 meter

w = 2 pi f = 2 pi/T = sqrt (k/m)

2 pi/12 = sqrt (k/.69)

.5236 = sqrt(k/.69)

.2742 = k/.69

k = .189 Newtons/meter

w = .5236 radians/second we know already

Xmax = 1.2 meter, we know that too

so

x = 1.2 cos (.5236 t) meters

w = w2 = w3

the frequency of v and a is THE SAME as for the position!

then

v = -1.2*.5236 * sin(.5236 t)

so Vmax = -.6283 m/s

a = -1.2 * .5236^2 cos (.5236 t)

= - w^2 x

amax = -1.2*.5236^2 = - .329 m/s^2

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