An apple weighs 1.11 N. When you hang it from the end of a long spring of force constant 1.53 N/m and negligible mass, it bounces up and down in SHM. If you stop the bouncing and let the apple swing from side to side through a small angle, the frequency of this simple pendulum is half the bounce frequency. (Because the angle is small, the back and forth swings do not cause any appreciable change in the length of the spring.)
What is the unstretched length of the spring (i.e., without the apple attached)?
I think these are the relevant ones:
For a normal spring, f = 1/2*pi ( sqrt (k/m ) )
for a simple pendulum, T = 2*pi * sqrt (L/g)
The Attempt at a Solution
For spring with apple, if mass of the apple is m, spring constant is k, then
mg = kx (using force); combining this with f = 1/2*pi ( sqrt (k/m) ) gives:
f = 1/(2*pi) ( sqrt (g/L) )
For simple pendulum, I think we have T = 2*pi* sqrt (L/g)
So i think we should then have: 2*pi* sqrt (L/g ) = 1/2 (1/2*pi) * sqrt (g/L), i.e.
L = g/(8 * pi^2).
However this is wrong and I am not sure why. (I don't know what the right answer is either).