# Simple harmonic motion of some mass

• jasonbans
In summary: So if the mass starts out at position P and displaces by +8.5cm to Q then the cycle is considered to have started at P+8.5 and ended at Q.

## 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?

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?

## 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.

I can provide a response to the content provided. The question is asking for the distance that the mass will move in the first five cycles of simple harmonic motion. This can be calculated using the equation for the amplitude of SHM, which is equal to the maximum displacement from equilibrium. In this case, the amplitude is given as 8.5 cm. Therefore, in the first five cycles, the mass will move a total distance of 8.5 cm x 5 = 42.5 cm. This assumes that the motion is ideal and there is no friction or other external forces acting on the mass. The question does not mention anything about rpm, so it is not relevant to the solution.

## 1. What is simple harmonic motion?

Simple harmonic motion is a type of periodic motion in which an object oscillates back and forth around an equilibrium point, such as a pendulum or a mass attached to a spring. The motion is described by a sinusoidal function and is characterized by a constant period and amplitude.

## 2. What factors affect the period of simple harmonic motion?

The period of simple harmonic motion is affected by the mass of the object, the spring constant, and the amplitude of the oscillation. It is also independent of the initial displacement and velocity of the object.

## 3. How does the force of a spring affect simple harmonic motion?

The force of a spring is directly proportional to the displacement of the object from its equilibrium position. This means that as the object moves further away from the equilibrium, the force of the spring pulling it back increases, creating a restoring force that causes the object to oscillate.

## 4. Can simple harmonic motion occur in other systems besides a spring and mass?

Yes, simple harmonic motion can occur in other systems such as a pendulum, a vibrating guitar string, or a swinging pendulum. As long as there is a restoring force that is proportional to the displacement of the object, simple harmonic motion can occur.

## 5. How is simple harmonic motion related to energy?

In simple harmonic motion, the total energy of the system is conserved and is constantly oscillating between kinetic and potential energy. At the equilibrium point, the energy is entirely potential and at the maximum displacement, the energy is entirely kinetic.