Simple Harmonic motion

2009-11-29 2:50 am
When i am doing some question about S.H.M,there are one kind of question
making me confusing.

In S.H.M ,some load is dropped into the object,the amplitude of S.H.M will

decrease.It can be proved by conservation of momentum.But if the

amplitude decrease,there are some energy lost,where are the energy

going?.My teacher tell me it may lose in form of sound energy when it was

dropped.But in my calculation,it is not related to the height of dropping.Even

i pull it lightly,by conservation of momentum, A will decrease.

Prove:

v1=initial max velocity. v2=final max velocity

m1v1=m2v2

A1=initial Amplitude A2=final Amplitude

Initial energy=0.5x k x A1=0.5 m1 v1^2

Final energy=0.5 x k x A2=0.5 m2 v2^2.

0.5 m2 v2 v2=Initial E x v2

As m2 increase,so v2 decrease.

So final energy is lower,so a2 is lower.

The energy is lost in form of?
更新1:

How to explain it if the energy is lost in form of heat even if i pull it lightly? Please explain it as detail,a full description to procedures of lossing energy.

回答 (1)

2009-12-04 6:30 am
✔ 最佳答案
As in situations involving collisions, when the load is dropped onto the oscillation object, there is impact and the collision is not elastic. Energy is lost as heat.

There is some mistake in your derivation, though the conclusion is right.
Using the same symbols as yours,

Initial energy = (1/2)k.A1^2 = (1/2)m1.v1^2
Final energy = (1/2)k.A2^2 = (1/2).m2.v2^2
Dividing: [A2/A1]^2 = (m2.v2).v2/(m1.v1).v1

But m2.v2 = m1.v1
hence, [A2/A1]^2 = (m1.v1).v2/(m1.v1).v1 = v2/v1

Because v2 would decrease after the load is added, so A2 would also decrease.



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