# Need help on harmonic motion problems

• killerb3756
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.
killerb3756

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!

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.

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

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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