Mass Spring Oscillator question

In summary, a 0.3kg mass is hung from a 0.8m vertical spring with an unstretched length of 0.65m. The mass is pulled down to a length of 0.9m and given an initial speed of 1.2m/s upwards. The spring constant is found to be 196Nm and the potential energy of the mass due to the spring is 24.5J. The next step is to consider the velocity of the mass at its bottom-most point and use the principle of energy conservation in the system.
  • #1
LocalStudent
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Homework Statement


A mass of 0.3kg hangs motionless from a vertical spring whose length is 0.8m and unstreteched length is 0.65m.

The mass is then pulled down so the spring has the length of 0.9m and given an initial speed upwards of 1.2m/s upwards.

What is the maximum length of the spring during the subsequent motion?





The Attempt at a Solution


I started by working out the spring constant.
Fgrav = Fspring when the mass is constant
using that I got the spring constant to be 196Nm

Then after that I'm not sure what to do..

I tried working out the potential energy on the mass due to the spring. My answer for that is 24.5J
 
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  • #2
The idea of working out the spring constant first is correct :smile:

Now, what happens to its velocity of the block when it reaches its bottom-most point?
Then think of energy conservation of the system.
 
  • #3
Thanks, Infinitum.
 

FAQ: Mass Spring Oscillator question

What is a Mass Spring Oscillator?

A Mass Spring Oscillator is a physical system consisting of a mass attached to a spring that is undergoing simple harmonic motion. It is a common model used in physics to study the behavior of oscillating systems.

How does a Mass Spring Oscillator work?

A Mass Spring Oscillator works by utilizing the force of the spring to create oscillations in the attached mass. As the mass moves away from its equilibrium position, the spring exerts a restorative force that pulls it back towards the equilibrium position. This back and forth motion continues, creating a periodic oscillation.

What factors affect the behavior of a Mass Spring Oscillator?

The behavior of a Mass Spring Oscillator is affected by several factors, including the mass of the object, the stiffness of the spring, and the amplitude of the oscillation. The frequency of the oscillation is also determined by these factors.

How is the motion of a Mass Spring Oscillator described mathematically?

The motion of a Mass Spring Oscillator can be described mathematically using the equation: x(t) = A * cos(ωt + φ), where x is the displacement of the mass from its equilibrium position at time t, A is the amplitude of the oscillation, ω is the angular frequency, and φ is the phase offset.

What are some real-world applications of Mass Spring Oscillators?

Mass Spring Oscillators have many real-world applications, including in clocks and watches, musical instruments, and shock absorbers in vehicles. They are also used in engineering and research to study the behavior of oscillating systems and to design structures that can withstand vibrations.

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