# Simple harmonic motion of some mass

## 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?

## The Attempt at a Solution

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

berkeman
Mentor

## 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?

## 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?

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

gneill
Mentor
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.