# SHM Question: What is the maximum extension of the spring?

• Alex Cooper
In summary, a 50g block is attached to a vertical spring with a stiffness constant of 9N/m and released from the unextended position. The maximum extension of the spring can be found using the formula Fsp=-kx. The time it takes for the block to reach the lowest point can be calculated using T=2pi(sqrtm/k). However, the division by two in the attempted solution is incorrect and a different value should be used. To find the maximum extension, a conservation of energy approach can be used with the relevant equations Fsp=-kx, KE=1/2mv^2, and Usp=mgh.
Alex Cooper

## Homework Statement

A 50g block is attached to a vertical spring whose stiffness constant is 9N/m. The block is released at the position where the spring is unextended. What is the maximum extension of the spring? How long does it take the block to reach the lowest point?

Fsp=-kx
T=2pi(sqrtm/k)
KE=1/2mv^2
Usp = mgh

## The Attempt at a Solution

I found the time it took to reach the lowest point but cannot seem to find the first portion of the question
Here is what I did for the time it took to reach the lowest point
T=2pi(sqrtm/k)
=2pi(sqrt0.05/9)
=0.468s/2
=0.23s

Last edited:
Hello Alex, Welcome to Physics Forums.

Alex Cooper said:
I found the time it took to reach the lowest point but cannot seem to find the first portion of the question
Here is what I did for the time it took to reach the lowest point
T=2pi(sqrtm/k)
=2pi(sqrt0.05/9)
=0.468s/2
=0.23s
You should be a bit more careful with your notation. When you introduced dividing by two in the second to last line, the quantity is no longer equal to the quantity above. You should also indicate the logic behind what you're doing with a comment.

That said, the division by two is not correct here. It's not a half cycle from the equilibrium point to an extreme. A half cycle would be a trip from equilibrium to extreme and then back to the equilibrium point (the block would then continue through the equilibrium point and continue upwards to a higher extreme point, then return to the equilibrium point to complete a full cycle). So choose another value other than "2".

For the distance to the lower extreme, consider a conservation of energy approach. Your Relevant equations did not include the potential energy for a spring, but you should have that in your text or notes.

## 1. What is SHM?

SHM stands for Simple Harmonic Motion. It is a type of periodic motion where the restoring force is directly proportional to the displacement from the equilibrium position.

## 2. What factors affect SHM?

The factors that affect SHM include the mass of the object, the stiffness of the spring, and the amplitude of the oscillation.

## 3. What is the equation for SHM?

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

## 4. How is the maximum extension of a spring related to SHM?

The maximum extension of a spring is directly related to the amplitude of SHM. As the amplitude increases, the maximum extension of the spring also increases.

## 5. How is SHM used in real life?

SHM is used in many real-life applications, such as pendulums, springs, and musical instruments. It is also used in engineering to design structures that can withstand vibrations and oscillations.

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