# Using Simple Harmonic motion and conservation of motion to find maximum velocity

• Fromaginator
In summary, the conversation discusses the relevant equations for a problem involving conservation of energy at the equilibrium point. It also mentions the average of two x values and how to calculate the maximum velocity at the lowest point. The conversation concludes with a reminder that all oscillations have two common factors and this information may be helpful for future problems.
Fromaginator
The Question

Relevant equations
KE=0.5*m*v^2
T=2*pi*sqrt(m/k)
EE=0.5*k*x^2
KEi+UEi=KEf+UEf
I think that's all of them

attempt at a solution
I was thinking about just using the conservation of energy at the the equilibrium point, as the kinetic energy would be at a max there and the potential energy would be at its minimum, Also the velocity would be at its max while the acceleration would be zero. However, one of the many problems I've run into on this question is that I'm unsure if the average of the two x values will give me the equilibrium point (if it did then it would be 5mm) and I don't feel comfrontable moving on having possibly made a false assumption.

I got the answer :) but for others what I did was
from the graph u can see that potential at highest point is 5J and at lowest point is 1J

mgh+ 1/2mU^2 = mgH + 1/2 mV^2 in this U = initial velocity = 0 and V = max velocity at lowest point and mgh is initial potential energy and mgH is potential energy at lowest point.
this gives
5 + 0 = 1 + (1/2 x (1.7/1000) x V^2) [ 1.7 is divided by 1000 to convert grams into kg]
V^2 = 4705.88
V = sqrt(4705.88)
V = 68.59 m/s

Remember one thing- All the oscillations have two things in common
I. the oscillation takes place about an equilibrium position and,
II. the motion is periodic.

These are the only two conditions that are to be fulfilled for a motion to be oscillatory motion.

Thanks I'll keep that in mind in similar problems, my finals coming up soon it may come in handy

## What is simple harmonic motion?

Simple harmonic motion is a type of periodic motion where an object moves back and forth along a straight line with a constant amplitude and frequency. It occurs when a restoring force is applied to an object that is proportional to its displacement from its equilibrium position.

## How is simple harmonic motion related to conservation of motion?

Simple harmonic motion is related to conservation of motion through the principle of conservation of energy. In simple harmonic motion, the total mechanical energy of an object (kinetic energy + potential energy) remains constant, as there is no external force acting on the system.

## How can simple harmonic motion be used to find maximum velocity?

To find the maximum velocity in simple harmonic motion, you can use the equation Vmax = Aω, where A is the amplitude of the motion and ω is the angular frequency. This equation shows that the maximum velocity is directly proportional to the amplitude of the motion and the angular frequency.

## What factors affect the maximum velocity in simple harmonic motion?

The maximum velocity in simple harmonic motion is affected by the amplitude of the motion, the angular frequency, and the mass of the object. A larger amplitude and higher angular frequency will result in a greater maximum velocity, while a larger mass will result in a smaller maximum velocity.

## Can simple harmonic motion be used to find the position of an object at any time?

Yes, simple harmonic motion can be used to find the position of an object at any time using the equation x = Acos(ωt + φ), where x is the position, A is the amplitude, ω is the angular frequency, t is the time, and φ is the phase angle. This equation represents the displacement from the equilibrium position at any given time.

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