# Simple Harmonic Motion and displacement

• IAmSparticus
In summary, the mass of the second block is 4 times the mass of the first block. This can be calculated by using the equation m2 = 4 m1, where m1 is the mass of the first block and m2 is the mass of the second block. The displacement of the spring increases by a factor of 5, leading to a new equation of m(9.8m/s/s) = k(5x). By solving for m, we get the mass of the second block to be 4 times the mass of the first block.
IAmSparticus
1. A 0.69 kg block is hung from and stretches a spring that is attached to the ceiling. A second block is attached to the first one, and the amount that the spring stretches from its unstrained length increases by a factor of 5. What is the mass of the second block?

2. Force= spring constant*displacement of spring from unstrained length

3. First off, I'm horrible at algebra so sorry if I make stupid mistakes in this attempt. The force is gravity so that becomes mg (.69kg*9.8 m/s/s).

mg=kx

If I pick a spring constant of 10 (does it matter what I pick?) then the equation becomes:

(.69kg)(9.8m/s/s)=10 x

Which would give a displacement of .6762 m. Now, when we increase it by a factor of 5, that displacement becomes 3.381 m. Plugging that into a new equations gives:

m (9.8m/s/s) = 10 (3.381m)

When I solve for m I get 3.45 kg, which is wrong. Someone tell me what I did wrong?

m is the total mass of the first and second blocks. Try to leave your work in symbols rather than substitute arbitrary numbers; its neater that way.

So if I leave it in the symbol format I get that (.69kg)(9.8m/s/s)=kx and m(9.8m/s/s)=k(5x). Now what?

(m1 + m2)g = 5 (kx) = 5 (m1)g
:. m2 = 4 m1

## 1. What is Simple Harmonic Motion?

Simple Harmonic Motion (SHM) is a type of periodic motion where the restoring force is directly proportional to the displacement from the equilibrium position and acts in the opposite direction of the displacement. This results in a motion that follows a sinusoidal pattern.

## 2. What is the equation for displacement in SHM?

The equation for displacement in SHM is x = A*cos(ωt + φ), where x is the displacement from equilibrium, A is the amplitude, ω is the angular frequency, and φ is the phase constant.

## 3. What is the difference between amplitude and displacement in SHM?

The amplitude in SHM refers to the maximum displacement from equilibrium, while displacement refers to the distance from equilibrium at any given time. Amplitude remains constant, while displacement changes over time.

## 4. How is the period of SHM related to the mass and spring constant?

The period of SHM is directly proportional to the square root of the mass and inversely proportional to the square root of the spring constant. This means that as the mass increases, the period increases, and as the spring constant increases, the period decreases.

## 5. What factors affect the frequency of SHM?

The frequency of SHM is affected by the mass, spring constant, and the amplitude of the motion. A higher mass or lower spring constant will result in a lower frequency, while a larger amplitude will result in a higher frequency.

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