How Do You Solve These Harmonic Motion Problems?

[killerb3756]

please help me with these two problems:

1. A meter stick is hung at its center from a thin wire It is twisted and oscillates with a period of 6.06 s. The meter stick is sawed off to a length of 72.4 cm. This piece is again balanced at its center and set in oscillation. With what period does it oscillate?

2. A 53.7 kg person jumps from a window to a fire net 20.4 m below, which stretches the net 1.19 m. Assume that the net behaves like a simple spring, and calculate how much it would stretch if the same person were lying in it.

for number one, I tried to set up a ratio T1/T2 = sqrt(I1/I2) where T1 is the period given and I am trying to find T2, but I=(1/12)ml^2 but I can't find the new mass for I2.

for number 2 I thought I could set up a energy equation where
mgh = (1/2)Kx^2 where x = 1.19 and h = 20.4, then I solved for K. once I got K I used K = mg/l to solve for l but I get the wrong answer. please help!

 

[Doc Al]

for number one, I tried to set up a ratio T1/T2 = sqrt(I1/I2) where T1 is the period given and I am trying to find T2, but I=(1/12)ml^2 but I can't find the new mass for I2.

You don't need the mass, just the ratio between the masses. If a meterstick (100 cm) has a mass of m, what must be the mass of the 72.4 cm piece? (Assume the meterstick has uniform density.)

for number 2 I thought I could set up a energy equation where
mgh = (1/2)Kx^2 where x = 1.19 and h = 20.4, then I solved for K. once I got K I used K = mg/l to solve for l but I get the wrong answer. please help!

Calculate the gravitational PE from the lowest point of the motion.

 

[killerb3756]

thanks I got the first one, but I still don't understand the second one. what do you mean the lowest point of motion?

 

[ninjagowoowoo]

See:

https://www.physicsforums.com/showthread.php?t=72546

find k using that equation, then calculate the distance with just the guy's weight. Don't forget about the gravitational potential energy... like i did.

 

[killerb3756]

thanks so much for your help.