Simple Harmonic Motion: Ball on Spring with Mass and Compression Calculation

[puhdanks]

The problem is a ball is dropped onto a spring and the spring compresses .95m. The ball then sticks to the spring and oscillates with a period of 1.1 seconds and has a mass of 6kg.



I thought that the equation mg(h+x)=1/2(k)(x^2) would be what i would use.



I got h=.47m I also figured out that k= 61.96N/M i tried using this equation for another problem and it did not work. I am not sure if this is the right answer. Also How would i find how much the spring would be compressed when the spring stopped oscillating and was at rest.

 

[guitarphysics]

What are you actually asked to find? You forgot to mention that. What do you mean by h? Always try to define whatever extra variables you use on here so people can understand what you mean.

 

[puhdanks]

opps sry lol i have to find from what height the ball was dropped from

 

[guitarphysics]

Ok, cool, that's better. Thanks. It seemed like that was the question, just wanted to make sure. How did you arrive at that result for k? You should have used the equation that tells you the period of a mass on a spring as a function of mass and spring constant. You can find it here: http://en.wikipedia.org/wiki/Simple_harmonic_motion#Mass_on_a_spring
I think that's the part you got wrong. The other part seems to be fine. Hope this helped, good luck.

 

[puhdanks]

I used k=F/x but when i use the equation T=2Pi(sqrt(M/K) i get a different answer

 

[guitarphysics]

How would you know F?

 

[guitarphysics]

Oh, I see what you did. You equaled the weight of the mass with the force that was being applied by the spring once the mass hit the bottom? That's not right, because when it's at the bottom, the mass *does* have an upwards acceleration (so the force from the spring is greater than its weight, not equal to it). The mass happens to have zero velocity, but its acceleration is certainly not zero. The other equation does hold, though.

 

[puhdanks]

I ended up getting .587m does that seem right?