Engery Conservation in Oscillatory Motion

[Julio Cesar]

A 0.980kg block slides on a frictionless, horizontal surface with a speed of 1.32m/s. The block encounters an unstretched spring with a force constant of 245N/m.

(a)How far is the spring compressed before the block comes to rest?

(b) How long is the block in contact with the spring before it comes to rest?



Equations: Conservation of energy using a spring.

E_i=E_f

1/2mv_o² = 1/2kA²

A= v_o√m/k

Question (b): T = 2∏√m/k




3. Attempt at solution shows:

A= 0.0835m

T= 0.397s

As far as the calculations, I know the amplitude as well as the period of one complete occilation. However, when the question asks me how long is the block in contact with the spring before it comes to rest...

Well, my senses tell me that it would be half a period since the spring is compressed when the block comes in contact with it and stops. (v= 0m/s)

The answer it gives me is 0.0993s...?!

Where does this come from; that's not half a period that's a quarter of a period. The answer may be staring at be straight in the face but I just don't get it. Can someone explain why the answer is 1/4 the period instead of 1/2 the period?

Thanks.

 

[ehild]

What is the time for zero displacement to maximum displacement during an SHM? http://hyperphysics.phy-astr.gsu.edu/hbase/shm.html

ehild

 

[Julio Cesar]

Wow! I feel like an idiot now. I've just spent the last hour just looking at the diagram, wondering why and didn't even think to draw out a sine function, lol!

Thanks so much, this helps out a ton!

 

[ehild]

A drawing always helps.

ehild