|
GR0177 #90
|
|
|
Problem
|
|
|
This problem is still being typed. |
Mechanics }Normal Modes
Note that  :
For figure 1, the potential energy is  . The kinetic energy is just  . Thus,  and  . Thus,  .
For figure 2, the potential energy is ^2) , since each spring travels only half as far. The kinetic energy is the same as in figure 1. Thus,  and . So, one has, 
Since  , the period /(2)}=1/2) , as in choice (A).
|
|
|
Alternate Solutions |
jax
2005-11-30 18:02:40 | Just remember that capacitors are analogous to springs, so springs and capacitors add in the same way.
Springs in series add like capacitors in series, etc. |  | sf001k
2005-11-10 21:09:52 | springs in series add like resistors in parallel, springs in parallel add like resistors in series. find k effective for system 1 and 2, then get the period. | |
|
|
Comments |
joy
2008-11-04 18:40:00 | I'm sorry but I don't understand why springs act like capacitors since k is equivalent to 1/C
Shoudln't it be
In series : 1/C1 + 1/C2 = 1/C k1 + k2 = k
In parallel C1 + C2 = C 1/k1 + 1/k2 = 1/k
?
Thanks for this awesome site |  | star
2008-03-01 04:03:29 | just remember that you need mor force for springs in parallel | | jax
2005-11-30 18:02:40 | Just remember that capacitors are analogous to springs, so springs and capacitors add in the same way.
Springs in series add like capacitors in series, etc.
poljen88
2007-10-27 12:26:12 |
The spring constant k is equivalent to 1/C, so it is the reverse. Springs acting in series are equivalent to capacitors acting in parallel.
|
Richard
2007-10-29 15:26:20 |
My thought exactly...
and if you don't remember the expression for  Yosun quoted, all you have to recall is that
 for springs (Hook's law) from which you can use 
to find the ratio of the periods ( ).
|
r10101
2007-11-02 17:27:29 |
jax is correct and poljen88 is not, that is, spring constants add in series/parallel in the same fashion as capacitance. That is, the opposite from the normal for resistors:
 (series)
 (parallel)
So for springs:
 (parallel)
 (series)
E.g. http://www.physics.brown.edu/physics/demopages/Demo/waves/demo/3a2020.htm
|
edhopkins
2009-06-28 19:48:12 |
Is it accurate to stake the assumption that both the effective spring constant adds in parallel and the distance traveled is half? It seems like one ought to come from the other. If you ignore the distance traveled you can still arrive at the ratio of periods purely by =  .
Offhand it seems that by inspection one could assume the distance traveled by the two springs in series is twice that of those in parallel, and intuitively reach the same conclusion.
|
| | sf001k
2005-11-10 21:09:52 | springs in series add like resistors in parallel, springs in parallel add like resistors in series. find k effective for system 1 and 2, then get the period. | | sf001k
2005-11-10 21:08:03 | | |
|
| Post A Comment! |
|
|
Bare Basic LaTeX Rosetta Stone
|
LaTeX syntax supported through dollar sign wrappers $, ex., $\alpha^2_0$ produces  .
|
| type this... |
to get... |
| $\int_0^\infty$ |
 |
| $\partial$ |
 |
| $\Rightarrow$ |
|
| $\ddot{x},\dot{x}$ |
 |
| $\sqrt{z}$ |
 |
| $\langle my \rangle$ |
 |
| $\left( abacadabra \right)_{me}$ |
_{me}) |
| $\vec{E}$ |
 |
| $\frac{a}{b}$ |
 |
|
|
|
|
|
