Need help on harmonic motion problems

In summary, a person jumps from a window to a net 20.4 meters below. The net stretches by 1.19 meters, so the person's weight is equivalent to the potential energy of the net.
  • #1
killerb3756
3
0
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!
 
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  • #2
killerb3756 said:
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.
 
  • #3
thanks I got the first one, but I still don't understand the second one. what do you mean the lowest point of motion?
 
  • #5
thanks so much for your help.
 

1. What is harmonic motion?

Harmonic motion is a type of periodic motion in which the object or system moves back and forth around a central equilibrium position, with a restoring force that is proportional to the displacement from the equilibrium position. Examples include a mass on a spring or a pendulum swinging back and forth.

2. How do you solve harmonic motion problems?

To solve harmonic motion problems, you typically use the equation x = A*cos(ωt + φ), where x is the displacement of the object, A is the amplitude, ω is the angular frequency, and φ is the phase angle. You may also need to use the equations for period T = 2π/ω and frequency f = 1/T to calculate the period and frequency of the motion.

3. What is the difference between simple harmonic motion and damped harmonic motion?

In simple harmonic motion, there is no external force acting on the object, resulting in a constant amplitude and frequency. In damped harmonic motion, there is an external force (such as friction or air resistance) that causes the amplitude and frequency to decrease over time.

4. How do you calculate the period and frequency of a harmonic motion?

The period T is the time it takes for one complete cycle of the motion and can be calculated using T = 2π/ω, where ω is the angular frequency. The frequency f is the number of cycles per second and can be calculated using f = 1/T.

5. What are some real-life examples of harmonic motion?

Some examples of harmonic motion in everyday life include the swinging of a pendulum, the motion of a mass on a spring, the vibration of a guitar string, and the motion of a swing in a playground. Harmonic motion can also be observed in the motion of planets around the sun and in the oscillation of molecules in a chemical bond.

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