# Solve Spring SHM Problem: Period of Oscillation in M1, M2, k

• brendan3eb
In summary, the problem involves two blocks connected by a spring and released from rest. The period of oscillation can be determined using the equation T=2PI*sqrt(m/k) and the force equation f=-kx. The equilibrium point remains the same and the problem can be solved by considering the positions of the masses and manipulating the equations to find the angular frequency.
brendan3eb

## Homework Statement

Two blocks of mass M2 and M1 (M2>M1) are connected by a spring with force constant k and are free to slide on a frictionless table. They are pulled apart and then released from rest. In terms of M1, M2, and k, what would the period of oscillation be?

T=2PI*sqrt(m/k)
f=-kx

## The Attempt at a Solution

So taking the starting position to be both blocks just before they released, one full cycle would be when they have both returned to their initial positions. Other than noting this, the problem leaves me perplexed as to what to do next..all I need is a hint in the right direction. I guess just picturing such an apparatus in my head is mind-boggling. Would the equilibrium point remain the same or would it start to expand and contract abnormally?

The CM wouldn't move, so you could start by taking that as the origin. Take x1 and x2 to be the positions of the masses etc. Now, write the force eqns on the springs. Take x=x1-x2, the dist between the two springs.

Your aim is to only find the w. Once you have reduced the two eqns to a form of Mx'' = -k'x, for some M, then directly you can find w. A bit of algebraic manipulation is reqd.

As a scientist, your first step should be to identify the variables and parameters in the problem. In this case, the variables are M1, M2, and k and the parameter is the period of oscillation, T.

Next, you should recall the equation for the period of oscillation of a mass-spring system, which is T=2π√(m/k). This equation relates the period of oscillation to the mass and spring constant.

Now, you need to apply this equation to the given problem. Remember that the blocks are connected by the spring, so the total mass in the system is M1+M2. Therefore, the period of oscillation will be T=2π√((M1+M2)/k).

To check if this is the correct solution, you can do a quick sanity check. If M1 is very small compared to M2, the period of oscillation should be close to the period of a single block attached to the spring, which is T=2π√(M2/k). This makes sense because if one block is much smaller, it will have a smaller effect on the period of oscillation.

In terms of the equilibrium point, it will remain the same as the blocks will oscillate around it. As long as the spring remains in the linear region of its force-displacement curve, the blocks will oscillate harmonically. It may help to draw a diagram or create a mental image of the system to better understand the motion.

I hope this helps guide you in the right direction. Remember to always start by identifying the variables and equations that relate them, and then apply them to the given problem. Good luck!

## 1. What is a spring SHM problem?

A spring SHM (simple harmonic motion) problem involves calculating the period of oscillation of a spring system, which is the time it takes for the spring to complete one full cycle of movement. This type of problem is commonly encountered in physics and engineering.

## 2. What factors affect the period of oscillation in a spring SHM problem?

The period of oscillation in a spring SHM problem is affected by the masses of the objects attached to the spring (M1 and M2) and the stiffness of the spring (k). In general, a higher mass will result in a longer period, while a stiffer spring will have a shorter period.

## 3. How do you solve for the period of oscillation in a spring SHM problem?

To solve for the period of oscillation in a spring SHM problem, you can use the formula T = 2π√(m/k), where T is the period, m is the total mass attached to the spring, and k is the spring constant. You may need to rearrange the formula if you are given different variables or need to solve for a different quantity.

## 4. Can you use the same formula to solve for the period of oscillation in different types of spring systems?

Yes, the formula T = 2π√(m/k) can be used to solve for the period of oscillation in any spring system, as long as you have the correct values for the mass and spring constant. This includes both horizontal and vertical spring systems, as well as systems with multiple springs attached in series or parallel.

## 5. What units should be used for the variables in the formula for the period of oscillation?

The variables in the formula for the period of oscillation should be in standard SI units. This means that the mass should be in kilograms (kg) and the spring constant should be in newtons per meter (N/m). The resulting period will be in seconds (s).

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