# Simple harmonic movement problem

• Cyannaca
In summary, the conversation is about finding the amplitude at which a mass will come off a piston during vertical S.H.M., as well as the maximum frequency at which the mass will remain on the piston. The key points to consider are using the correct units and equations for acceleration, and the relationship between acceleration and displacement. The answer for the amplitude is 25 cm, and for the maximum frequency it is 2.24 Hz. There is also a discussion about using the correct units for gravity and how to find the equation for acceleration. Additionally, there is a question about why the answer for the amplitude is exactly double for question a. It is explained that this is because the acceleration is maximum at the maximum displacement, and the equation for this

#### Cyannaca

I would really need help on these questions.

A mass is on a piston that oscillates vertically describing a S.H.M. T= 1s.

1-At which amplitude does the mass comes off the piston?
The answer is supposed to be 25 cm but I don't know how to find the position of the mass when it comes off the piston. I found w but I couldn't write the equation.

2- If the amplitude was 5 cm, what would be the maximum frequency so that the mass remains on the piston?

Hint
The mass will leave the piston when the normal reaction between will be zero. This will happen when the acceleration of the piston is more then acceleration due to gravity.

Listen to mukundpa he put you on the right track but I want to add a couple of things.

1) Make sure your units match. If you use gravity in m/s^2 your distances must be in meters. (otherwise you can convert gravity to cm/s^2) same thing.

2) You need an eqn. for acceleration
b) if you do not have an eqn for accelration here is how to get one.
(I did this whole thing by comparing shm to circular motion)
Assume that the greatest acceleration is when the piston starts to go down (this drops out any sin from your eqn). Now use centripital acceleration and substitute for velocity (period and frequency will take its place)

3) No need to use w (omega), but it will help the 2Pi disappear.

The answer to b) seems to be 2.24Hz and not 2,24 Hz as you have written.
I got this from the equation Aw^2=g

Thanks for the help but now I have another question. This is probably stupid but I can't figure out why I get exactly the double for question a. I get 0.49m and the pulsation is equal to 2pi.

Acceleration is maximum when the displacement is maximum(amplitude). For minimum amplitude for which the mass just leaves the piston the max. acceleration is g at the max. displacenrnt. Thus

w^2A = g
A = g/4Pi^2 = 9.8/4*9.87 = 0.248m which is close to 25 cm

some time g in m/s/s and pi^2 both are approximated to 10

## 1. What is simple harmonic motion?

Simple harmonic motion is a type of periodic motion in which an object oscillates back and forth around a central equilibrium point. It is characterized by a constant amplitude and a sinusoidal (sine or cosine) pattern of movement.

## 2. What are the key components of a simple harmonic motion problem?

The key components of a simple harmonic motion problem are the mass of the object, the spring constant of the system, and the amplitude and period of the oscillation.

## 3. How is the period of a simple harmonic motion calculated?

The period of a simple harmonic motion can be calculated using the equation T = 2π√(m/k), where T is the period, m is the mass of the object, and k is the spring constant of the system.

## 4. Can simple harmonic motion problems be solved using energy conservation?

Yes, simple harmonic motion problems can be solved using energy conservation principles. The total mechanical energy of the system (kinetic energy + potential energy) remains constant throughout the oscillation.

## 5. How does amplitude affect the frequency of a simple harmonic motion?

The amplitude of a simple harmonic motion does not affect the frequency, which is the number of oscillations per unit time. The frequency is only affected by the mass and spring constant of the system.

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