Oscillations and mechanical energy

In summary, the system being discussed is a mass-spring system with an amplitude of 3.30 cm, a spring constant of 231 N/m, and a mass of 537 g. The problem at hand is to determine the mechanical energy of the system. It is mentioned that mechanical energy is the sum of potential energy and kinetic energy. The equation for the energy stored in a compressed or extended spring is discussed, and it is clarified that the maximum amplitude is the delta x value needed for the equation. It is also noted that at maximum amplitude, the velocity is zero, resulting in only potential energy being present in the system.
  • #1
Knfoster
45
0

Homework Statement



A mass-spring system oscillates with an amplitude of 3.30 cm. If the spring constant is 231 N/m and the mass is 537 g, determine the mechanical energy of the system.


Homework Equations



Mechanical energy is potential energy plus kinetic energy

The Attempt at a Solution



How do I go about starting this problem?
 
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  • #2
Are you familiar with the equation for the energy stored in a compressed (or extended) spring, in terms of k and delta-x?
 
  • #3
1/2*k*delta x but I'm not given delta x am I? or is the amplitude delta x? and if it is then what do I use for velocity in the 1/2 mv^2 ?
 
  • #4
it's 1/2*k*delta x squared. The max amplitude is your delta x, and since you're considering the situation at max amplitude, the velocity is zero, and so you have just potential energy.

Good luck!
Arjun
 
  • #5
Thank you
 

FAQ: Oscillations and mechanical energy

1. What is oscillation?

Oscillation refers to a repetitive motion or movement around an equilibrium point. This can be seen in objects that move back and forth or up and down continuously.

2. What is mechanical energy?

Mechanical energy is the sum of potential and kinetic energy in a system. Potential energy is the energy an object has due to its position or state, while kinetic energy is the energy an object has due to its motion.

3. How are oscillations and mechanical energy related?

Oscillations involve the transfer of energy between potential and kinetic energy. As an object oscillates, it moves between states of potential and kinetic energy, resulting in a continuous cycle of energy transfer.

4. What are some real-world examples of oscillations and mechanical energy?

Some common examples include a pendulum, a spring, a swinging door, and a bouncing ball. All of these objects exhibit oscillatory motion and involve the transfer of mechanical energy.

5. How can we calculate the mechanical energy of an oscillating system?

The mechanical energy of an oscillating system can be calculated using the equation E = K + U, where E is the total mechanical energy, K is the kinetic energy, and U is the potential energy. The values for K and U can be calculated using the equations for kinetic energy (K = 1/2mv^2) and potential energy (U = mgh), respectively.

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