Energy and Simple Harmonic Motion - Part II.

In summary, the speed of the object at the instant when the spring is stretched by 0.037 m relative to its unstrained length is 0.601 m/s. This can be found by using Hooke's law and conservation of energy, with the given values of horizontal spring compression, angular frequency, and spring constant.
  • #1
sailordragonball
43
0
A horizontal spring is lying on a frictionless surface. One end of the spring is attached to a wall whle the other end is connected to a movable object. The spring and object are compressed by 0.064 m, released from rest, and subsequently oscillate back and forth with an angular frequency of 11.5 rad/s. What is the speed of the object at the instant when the spring is stretched by 0.037 m relative to its unstrained length?

... I tried using KEo + PEo + SPEo = KEf + PEf + SPEf ... but, I can't get anywhere ...

... I found out that the frequency is 18.05hz and it's relative time is .056 seconds - and that's where I'm stuck!
 
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  • #2
Use Hooke's law and conservation of energy.
 
  • #3
Do I set them equal to each other??

... I don't understand the .64 meter compression part ... does that equal "X" in Hooke's Law and in ?
 
  • #4
Hint -- Can you find the value of the spring constant?

BTW -- you are right in that the compression WILL be X in hooke's Law.
 
  • #5
I figured it out ...

A = 0.064m (given in the problem)
omega = 11.5 (rad/s) - given in the problem
x = 0.037m (given in the problem)V(max) = A(omega)
V(max) = 0.064(11.5)
V(max) = .736(m/s)

V = V(max) * [the square root of the quantity of (1- {[x^2]/[A^2]})]
V = .736 * [the square root of the quantity of (1- {[0.037^2]/[0.064^2]})]

V = 0.601 (m/s)
 

1. What is the relationship between energy and simple harmonic motion?

In simple harmonic motion, energy is constantly being converted between potential energy and kinetic energy. As the object moves towards the center of its oscillation, potential energy increases while kinetic energy decreases. As it moves away from the center, the opposite occurs.

2. How does the amplitude of a simple harmonic motion affect its energy?

The amplitude of a simple harmonic motion does not affect its energy. The total energy of a simple harmonic motion is determined by the mass, spring constant, and maximum displacement from equilibrium, but not the amplitude.

3. How does the period of a simple harmonic motion affect its energy?

The period of a simple harmonic motion does not affect its energy. The energy of a simple harmonic motion is determined by the physical properties of the system, not its time period.

4. Can energy be lost in a simple harmonic motion?

No, energy is conserved in a simple harmonic motion. The total energy remains constant as it is converted between potential and kinetic energy.

5. How is the potential energy of a simple harmonic motion related to the spring constant?

The potential energy of a simple harmonic motion is directly proportional to the square of the spring constant. In other words, as the spring constant increases, so does the potential energy of the system.

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