Simple harmonic motion of some mass

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SUMMARY

The discussion centers on the simple harmonic motion (SHM) of a 0.25-kg mass attached to a spring with a force constant of 1.4 x 10² N/m, displaced 8.5 cm. The mass undergoes SHM, and one complete cycle is defined as the mass returning to its initial position with zero velocity. The conversation highlights the importance of understanding the system's constraints, such as whether the motion is horizontal on a frictionless plane or if the mass can swing freely. The participants clarify that in a frictionless scenario, the amplitude remains constant across cycles.

PREREQUISITES
  • Understanding of simple harmonic motion (SHM)
  • Knowledge of mass-spring systems and force constants
  • Familiarity with the concept of cycles in oscillatory motion
  • Basic principles of friction and energy loss in mechanical systems
NEXT STEPS
  • Study the mathematical equations governing simple harmonic motion
  • Learn about the effects of friction on oscillatory systems
  • Explore graphical representations of SHM, including displacement-time graphs
  • Investigate the energy transformations in mass-spring systems during oscillation
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and oscillatory motion, as well as educators seeking to clarify concepts related to simple harmonic motion and mass-spring systems.

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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