Simple harmonic motion of some mass

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Homework Help Overview

The discussion revolves around a mass-spring system undergoing simple harmonic motion (SHM). A 0.25-kg mass is attached to a spring with a force constant of 1.4 x 10^2 N/m and is displaced 8.5 cm from its equilibrium position. The question posed is about the distance the mass moves in the first five cycles of motion.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants express uncertainty regarding the meaning of "the first five cycles," with one questioning whether it refers to revolutions per minute (rpm). Others seek clarification on the setup, including the presence of a frictionless plane and the nature of the mass's motion.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem and questioning the assumptions regarding the system's setup. Clarifications about the definition of a cycle in the context of SHM are being discussed, particularly in relation to friction and energy loss.

Contextual Notes

There is a noted lack of a diagram to clarify the system's configuration, which may affect the understanding of the motion involved. The implications of friction on the definition of a cycle are also under consideration.

jasonbans
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Homework Statement


A 0.25-kg mass is attached to the end of a spring that is attached horizontally to
a wall. When the mass is displaced 8.5 cm and then released, it undergoes SHM.
The force constant of the spring is 1.4 3 102 N/m. The amplitude remains
constant.
(a) How far does the mass move in the first five cycles?

Homework Equations





The Attempt at a Solution


not sure what the question mean the first 5 cycles is that the rpm?
 
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jasonbans said:

Homework Statement


A 0.25-kg mass is attached to the end of a spring that is attached horizontally to
a wall. When the mass is displaced 8.5 cm and then released, it undergoes SHM.
The force constant of the spring is 1.4 3 102 N/m. The amplitude remains
constant.
(a) How far does the mass move in the first five cycles?

Homework Equations





The Attempt at a Solution


not sure what the question mean the first 5 cycles is that the rpm?

Yeah, that makes no sense without a diagram. Is there a frictionless plane under the mass supporting it so all of its motion is horizontal? Or is it free to swing down and hit the wall or something?
 
berkeman said:
Yeah, that makes no sense without a diagram. Is there a frictionless plane under the mass supporting it so all of its motion is horizontal? Or is it free to swing down and hit the wall or something?

which the spring is attached to the wall horizontally meaning the object will move in the x-axis
 
One cycle is complete when a system returns to the same state that marked the beginning of the cycle. In the case of a mass-spring system (without friction), if the mass is in some given location with some given velocity, the cycle is complete when it again has that position and velocity. So if you start counting a cycle with the mass displaced by +8.5cm and zero velocity then one cycle is complete when the mass returns to +8.5cm and has zero velocity.

When friction is involved you have to be a bit more careful in defining a cycle because amplitude will diminish during each one as energy is lost. It's often easier to measure a cycle from peak displacement to (same sign) peak displacement, or by successive crossings of the equilibrium point in the same direction.
 

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