Pendulum Period change due to gravitational force change

[Sekonda]

Hey,

I was wondering how to go about a pendulum problem, basically if we have a clock pendulum that oscillates with period 2s unaffected; if we add a large mass on the floor, so that the pendulum experiences some small extra gravitational force towards the floor.

Now I have determined this force and therefore the extra vertical acceleration due to this added floor mass but I now have to determine how this affects the period.

So provided I know the extra vertical acceleration, how do I determine the effect this has on the period?

Thanks guys!

 

[LawrenceC]

I misread the problem. Comment deleted.

 

[LawrenceC]

The period of a pendulum for small oscillation is

P = 2*pi*sqrt(l/g)

where l is pendulum length and g is acceleration of gravity.

 

[Sekonda]

So based on the fact that the length doesn't change it is safe to assume that period is inversely proportional to the square root of the acceleration and so it's just a case of using the new acceleration and the initial 'g' acceleration to find the difference in the periods.

I think this is most probably the way to go about the problem; though correct me if I'm wrong.

Thanks for the help!
S

 

[Dadface]

I suggest you do a few rough calculations first.Think of the largest mass you could concievably put on the floor,work out how this would change the value of g and then work out whether a simple pendulum would be sensitive enough to detect the extremely small change of time period that this added mass would bring about.

 

[Sekonda]

Ahh I've only just seen your comment Dadface, clever idea; I "think" I've got the problem solved so I'll try doing that to see if my answer is reasonable.

Thanks,
S