# MHS exercises

## MHS Strength

1. What is the force exerted on a 0.3m-mass, 0.5kg-mass spring oscillator having a period of 3 seconds at the moment when its elongation is maximum?

Using the equation:

Remembering that:

And that, at the moment where the elongation is maximum:

x = A

We can write the force equation:

2. What is the frequency of an oscillator that has a pulsation ω = π?

Using:

We will find that the period of the movement is:

Knowing that the frequency equals the inverse of the period:

## Spring Mass Oscillator

1. What should be the elastic constant of a spring so that, when placed on a horizontal spring-mass oscillator, considering the maximum allowable force equal to 100N, it can support a movement of a mass of 2kg in an amplitude of 1m?

Using the force equation, remembering that for spring mass ocilators the constant k equals the spring elastic constant we have:

For this case we will use the values ​​of maximum elongation (amplitude) and highest allowable force (remembering that this will be restorative, therefore negative), thus:

## Simple pendulum

1. What is the period and frequency of a single pendulum, which is 0.25m long? Consider g = 10m / s².

Using the equation:

Overriding the given values:

Knowing that the frequency equals the inverse of the period: