Energy conservation in oscillatory motion

In summary, using the formula (1/2)mv^2= (1/2)kd^2 and the given values of mass, force constant, and displacement, the speed of the mass when it is .128 m from equilibrium is found to be 1.43 m/s. This was done by equating the mechanical energies at two different states of the system and solving for the unknown velocity.
  • #1
mansfief
1
0

Homework Statement



A 0.321-kg mass is attached to a spring with a force constant of 13.3 N/m. If the mass is displaced .256 m grom the equilibrium and released, what is its speed when it is .128 m from equilibrium. The answer is 1.43 m/s

Homework Equations



k=(w^2)m
w=2pi/T

The Attempt at a Solution


I used the formula (1/2)mv^2= (1/2)kd^2. I solved for k and got 6.44 rad/s and then i solved the equation for v. I then used .128 for my d. I plugged in my answer and got 8.24. I also used d as .256 and got 1.64
 
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  • #2
k is given as 13.3

here's how energy conservation works

for one state of system ... write all mechanical (potential + kinetic) energies associated with it
the do same for other state
the 2 energies shall be same so equate them and find unknown

so here find energy when spring is initially stretched and when it has extension .128 and equate them
 

Related to Energy conservation in oscillatory motion

1. What is energy conservation in oscillatory motion?

Energy conservation in oscillatory motion refers to the principle that the total energy of a system undergoing oscillatory motion remains constant. This means that the sum of potential energy and kinetic energy at any point in the motion will always be the same, regardless of the position or velocity of the object.

2. Why is energy conservation important in oscillatory motion?

Energy conservation is important in oscillatory motion because it allows us to predict and understand the behavior of the system. It also helps us to analyze the efficiency of the system and identify any losses of energy due to friction or other factors.

3. How is energy conserved in oscillatory motion?

Energy is conserved in oscillatory motion because the total mechanical energy (kinetic energy + potential energy) remains constant throughout the motion. As the object moves back and forth, its potential energy is converted into kinetic energy and vice versa, but the total amount of energy remains unchanged.

4. What are some examples of energy conservation in oscillatory motion?

Some common examples of energy conservation in oscillatory motion include a simple pendulum, a mass on a spring, and a child on a swing. In each of these cases, the total energy of the system remains constant, even as the object moves back and forth.

5. How does energy conservation affect the amplitude and frequency of oscillatory motion?

According to the principle of energy conservation, the amplitude and frequency of oscillatory motion are inversely proportional. This means that as the amplitude increases, the frequency decreases, and vice versa. This relationship is governed by the total energy of the system, which remains constant throughout the motion.

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