Simple harmonic motion in a string

In summary, a particle attached to a light elastic string with a natural length of 50 cm and modulus of 20 N is released from rest at a distance of 60 cm from the fastened end. Using the equation T=kx/l, where T is tension, k is the modulus, x is the displacement, and l is the length, we can determine that the acceleration of the particle is -100x. After being released, the particle will take a quarter of a cycle to reach its natural length, then move unimpeded to O and beyond. The time it takes to reach O can be found using the equation T=2pi/w, where w is the angular velocity.
  • #1
aurao2003
126
0

Homework Statement


Hi
I need some clarification on this question
A light elastic string of natural length 50 cm and modulus 20 N has one end fastened to O on a smooth horizontal table. The other end has a particle of mass 0.4 kg attached to it and the particle is released from rest at a distance 60 cm from O. Find the time it takes to reach O.


Homework Equations





The Attempt at a Solution


While the string is stretched
T=kx/l
=20x/0.5
=40x
40x=-.4a
So,a = -100x

w=10
T=2pi/10 =pi/5

I get stuck from here. Can anyone help please? Thanks
 
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  • #2
Think about how the mass moves after it's released. If the string were a spring, the mass would take a quarter of a cycle to return to its natural length, another 1/4 cycle to get to its farthest point, and 1/2 cycle to come back.

However, this is a string, which means it can't resist any compression. The mass would take 1/4 cycle for the string to return to its natural length. After that, the mass moves unimpeded all the way to O and beyond.
 
  • #3
Thanks a lot guys! Sorry for late reply.
 

What is simple harmonic motion in a string?

Simple harmonic motion in a string refers to the back-and-forth movement of a string in a regular pattern, where the string moves in a straight line and its velocity and acceleration are proportional to its displacement from the equilibrium position.

What is the equation for simple harmonic motion in a string?

The equation for simple harmonic motion in a string is y = A sin(ωt + φ), where y is the displacement from the equilibrium position, A is the amplitude (maximum displacement), ω is the angular frequency, and φ is the phase constant.

What factors affect the frequency of simple harmonic motion in a string?

The frequency of simple harmonic motion in a string is affected by the mass of the string, the tension in the string, and the length of the string. The frequency is higher for strings with lower mass, higher tension, and shorter length.

How does damping affect simple harmonic motion in a string?

Damping, which is the gradual decrease in amplitude over time, can affect simple harmonic motion in a string by decreasing the frequency and increasing the period of the motion. This is because damping reduces the total energy of the system, causing the string to lose energy and decrease its amplitude.

What applications does simple harmonic motion in a string have?

Simple harmonic motion in a string has many applications, including musical instruments such as guitars and violins, pendulums in clocks, and seismometers for detecting earthquakes. It is also used in various scientific experiments and studies.

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