Finding mechanical energy of simple harmonic oscilator

In summary, when a block of mass 45 g attached to a spring with a spring constant of 240 N/m is displaced 3.5 cm from its equilibrium position and released with an initial velocity of 2.5 m/s, its total energy is 0.29 J.
  • #1
Dalip Saini
16
0

Homework Statement



A simple harmonic oscillator consists of a block of mass 45 g attached to a spring of spring constant 240 N/m, oscillating on a frictionless surface. If the block is displaced 3.5 cm from its equilibrium position and released with an initial velocity of 2.5 m/s, what is its total energy?
  • A

    0.15 J
  • B

    The total energy varies during each cycle of oscillation.
  • C

    0.20 J
  • D

    0.29 J
  • E

    0.14 J

Homework Equations


E = 0.5kx^2+0.5mv^2

The Attempt at a Solution


I plugged in the values into the formula and I got 0.14J but the answer is 0.29J
 
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  • #2
Dalip Saini said:

Homework Statement



A simple harmonic oscillator consists of a block of mass 45 g attached to a spring of spring constant 240 N/m, oscillating on a frictionless surface. If the block is displaced 3.5 cm from its equilibrium position and released with an initial velocity of 2.5 m/s, what is its total energy?
  • A

    0.15 J
  • B

    The total energy varies during each cycle of oscillation.
  • C

    0.20 J
  • D

    0.29 J
  • E

    0.14 J

Homework Equations


E = 0.5kx^2+0.5mv^2

The Attempt at a Solution


I plugged in the values into the formula and I got 0.14J but the answer is 0.29J
What values did you plug into the formula?
 
  • #3
k=240 N/m
x=0.035m
m=0.045
v = 2.5 m/s
 
  • #4
Actually I just plugged in the values again and I got the answer. Sorry about that
 

Related to Finding mechanical energy of simple harmonic oscilator

1. What is mechanical energy in the context of a simple harmonic oscillator?

Mechanical energy in a simple harmonic oscillator refers to the sum of kinetic and potential energy of the system. It is a measure of the energy that is constantly being exchanged between kinetic and potential energy as the oscillator vibrates.

2. How do I calculate the mechanical energy of a simple harmonic oscillator?

The mechanical energy of a simple harmonic oscillator can be calculated using the equation: E = 1/2 * m * v^2 + 1/2 * k * x^2, where m is the mass of the oscillator, v is the velocity, k is the spring constant, and x is the displacement from equilibrium. This equation takes into account both kinetic and potential energy.

3. Is the mechanical energy of a simple harmonic oscillator constant?

Yes, the mechanical energy of a simple harmonic oscillator remains constant throughout its motion. This is because the total energy of the system is conserved, and the energy is constantly being exchanged between kinetic and potential energy.

4. How does the mechanical energy of a simple harmonic oscillator change with amplitude?

The mechanical energy of a simple harmonic oscillator is directly proportional to the square of the amplitude. This means that as the amplitude increases, the mechanical energy also increases. However, the total energy of the system remains constant.

5. Can the mechanical energy of a simple harmonic oscillator be negative?

No, the mechanical energy of a simple harmonic oscillator cannot be negative. This is because both kinetic and potential energy are always positive quantities. The sum of these two energies will always result in a positive value, representing the total mechanical energy of the system.

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